3463:. This commutativity isomorphism encodes the "rule of signs" that is essential to super linear algebra. It effectively says that a minus sign is picked up whenever two odd elements are interchanged. One need not worry about signs in the categorical setting as long as the above operator is used wherever appropriate.
1977:
1100:
294:
1392:
Every linear transformation, not necessarily grade-preserving, from one super vector space to another can be written uniquely as the sum of a grade-preserving transformation and a grade-reversing one—that is, a transformation
3981:
2740:
2633:
580:
4101:
1720:
2492:
3412:
1814:
3304:
3756:
4195:
1500:
1003:
2358:
2289:
1227:
4270:
3801:
3505:
3457:
3200:
3098:
3044:
3874:
3671:
3556:
1594:
1387:
3241:
2185:
890:
852:
2524:
2399:
1423:
1156:
193:
66:
4045:
3628:
2859:
1625:
1344:
4224:
4021:
3128:
2955:
2793:
2207:
100:
2913:
3827:
2128:
2101:
2074:
2023:
1806:
998:
990:
724:
697:
483:
456:
351:
324:
3141:
The categorical approach to super linear algebra is to first formulate definitions and theorems regarding ordinary (ungraded) algebraic objects in the language of
645:
or fermionic. Definitions for super vector spaces are often given only in terms of homogeneous elements and then extended to nonhomogeneous elements by linearity.
201:
815:
389:
3600:
3580:
2975:
2933:
2886:
2148:
2043:
1783:
1763:
1743:
1551:
1531:
1310:
1290:
1270:
1250:
964:
930:
910:
784:
764:
744:
666:
627:
603:
429:
409:
144:
124:
3882:
2639:
2532:
491:
4053:
4592:
4440:
1633:
4739:
4688:
2407:
4724:
4714:
1972:{\displaystyle \mathbf {Hom} (V,W)=\mathrm {Hom} (V,W)\oplus \mathrm {Hom} (V,\Pi W)=\mathrm {Hom} (V,W)\oplus \mathrm {Hom} (\Pi V,W).}
943:
that is spanned by homogeneous elements. Homogeneous subspaces are super vector spaces in their own right (with the obvious grading).
4693:
3315:
4399:
3249:
3679:
5022:
2369:
4112:
4734:
4409:
3145:
and then transfer these directly to the category of super vector spaces. This leads to a treatment of "superobjects" such as
4744:
17:
1431:
2295:
2226:
1164:
4433:
2217:
1987:
The usual algebraic constructions for ordinary vector spaces have their counterpart in the super vector space setting.
4379:
2769:
A common construction when working with super vector spaces is to enlarge the field of scalars to a supercommutative
4860:
4749:
4473:
4233:
3764:
3468:
3420:
3163:
3061:
4787:
4782:
4719:
4200:
Associativity and the existence of an identity can be expressed with the usual commutative diagrams, so that a
5017:
4426:
4371:
2983:
4385:
4767:
4683:
4652:
4607:
4468:
4357:
3836:
3633:
3518:
3460:
1556:
1349:
3209:
2153:
860:
820:
4667:
2865:
2500:
2375:
1396:
1129:
169:
42:
4637:
4521:
4026:
3605:
2801:
1602:
1323:
516:
4662:
4227:
3508:
3105:
2763:
4207:
4004:
3111:
2938:
2776:
2209:
thought of as a purely even super vector space) with the gradation given in the previous section.
2190:
83:
2891:
3806:
4772:
4622:
4526:
3101:
1119:
1095:{\displaystyle {\begin{aligned}(\Pi V)_{0}&=V_{1},\\(\Pi V)_{1}&=V_{0}.\end{aligned}}}
4802:
4797:
4709:
4647:
4551:
4531:
3206:
with the super tensor product as the monoidal product and the purely even super vector space
1123:
289:{\displaystyle V=V_{0}\oplus V_{1},\quad 0,1\in \mathbb {Z} _{2}=\mathbb {Z} /2\mathbb {Z} .}
4587:
4536:
3154:
2751:
2401:
comes into play. The underlying space is as in the ungraded case with the grading given by
2106:
2079:
2052:
2001:
1788:
972:
702:
675:
461:
434:
329:
302:
8:
4807:
4792:
4777:
4546:
3512:
2220:
of super vector spaces are constructed as in the ungraded case with the grading given by
792:
364:
151:
78:
70:
3976:{\displaystyle \mathrm {Hom} (U\otimes V,W)\cong \mathrm {Hom} (U,\mathbf {Hom} (V,W)).}
4916:
4483:
3585:
3565:
2960:
2918:
2871:
2133:
2028:
1768:
1748:
1728:
1536:
1516:
1295:
1275:
1255:
1235:
949:
915:
895:
769:
749:
729:
669:
651:
612:
588:
414:
394:
129:
109:
4405:
4404:. Courant Lecture Notes in Mathematics. Vol. 11. American Mathematical Society.
4395:
4375:
3203:
2770:
2046:
1122:
of super vector spaces, from one super vector space to another is a grade-preserving
992:
to be the super vector space with the even and odd subspaces interchanged. That is,
4617:
4516:
4503:
3150:
2755:
855:
4946:
4911:
4632:
4627:
3142:
2735:{\displaystyle (V\otimes W)_{1}=(V_{0}\otimes W_{1})\oplus (V_{1}\otimes W_{0}).}
2628:{\displaystyle (V\otimes W)_{0}=(V_{0}\otimes W_{0})\oplus (V_{1}\otimes W_{1}),}
940:
146:. The study of super vector spaces and their generalizations is sometimes called
4976:
575:{\displaystyle |x|={\begin{cases}0&x\in V_{0}\\1&x\in V_{1}\end{cases}}}
4966:
4951:
4597:
4582:
4353:
4201:
5011:
4991:
4971:
4921:
4556:
4493:
4463:
4449:
155:
39:
4096:{\displaystyle \mu :{\mathcal {A}}\otimes {\mathcal {A}}\to {\mathcal {A}},}
4996:
4981:
4941:
4931:
4926:
4817:
4759:
4642:
4511:
4478:
4106:
that is a super vector space homomorphism. This is equivalent to demanding
3998:
3992:
3830:
3146:
1111:
74:
4986:
4961:
4956:
4906:
4885:
4850:
4845:
4572:
4362:
2759:
1715:{\displaystyle \left(\mathbf {Hom} (V,W)\right)_{0}=\mathrm {Hom} (V,W).}
1313:
31:
4890:
4880:
4865:
4657:
4577:
4541:
1996:
103:
2487:{\displaystyle (V\otimes W)_{i}=\bigoplus _{j+k=i}V_{j}\otimes W_{k},}
4936:
4840:
4729:
1317:
3157:, etc. that is completely analogous to their ungraded counterparts.
4875:
4870:
4855:
4830:
3131:
1115:
912:
coordinate basis vectors and the odd space is spanned by the last
4835:
633:. In theoretical physics, the even elements are sometimes called
154:
where they are used to describe the various algebraic aspects of
4418:
4612:
4602:
3407:{\displaystyle \tau _{V,W}(x\otimes y)=(-1)^{|x||y|}y\otimes x}
4825:
3299:{\displaystyle \tau _{V,W}:V\otimes W\rightarrow W\otimes V,}
3751:{\displaystyle \mathrm {Hom} (V,W)=\mathbf {Hom} (V,W)_{0}.}
27:
Graded vector space with applications to theoretical physics
2045:
can be regarded as a super vector space by taking the even
568:
3138:
linear transformations (i.e. the grade preserving ones).
2758:, one may generalize super vector spaces over a field to
2750:
Just as one may generalize vector spaces over a field to
4190:{\displaystyle |ab|=|a|+|b|,\quad a,b\in {\mathcal {A}}}
1627:, the structure of a super vector space. In particular,
4368:
Quantum Fields and
Strings: A Course for Mathematicians
2372:
of super vector spaces. Here the additive structure of
3049:
4363:"Notes on Supersymmetry (following Joseph Bernstein)"
4236:
4210:
4115:
4056:
4029:
4007:
3885:
3839:
3809:
3767:
3682:
3636:
3608:
3588:
3568:
3521:
3471:
3423:
3318:
3252:
3243:
as the unit object. The involutive braiding operator
3212:
3166:
3114:
3064:
2986:
2963:
2941:
2921:
2894:
2874:
2804:
2779:
2642:
2535:
2503:
2410:
2378:
2298:
2229:
2193:
2156:
2136:
2109:
2082:
2055:
2031:
2004:
1817:
1791:
1771:
1751:
1731:
1636:
1605:
1559:
1539:
1519:
1505:
Declaring the grade-preserving transformations to be
1434:
1399:
1352:
1326:
1298:
1278:
1258:
1238:
1167:
1132:
1001:
975:
952:
918:
898:
863:
823:
795:
772:
752:
732:
705:
678:
654:
615:
591:
494:
464:
437:
417:
397:
367:
332:
305:
204:
172:
132:
112:
86:
45:
1982:
1495:{\displaystyle f(V_{i})\subset W_{1-i},\quad i=0,1.}
150:. These objects find their principal application in
2076:and the odd functionals to be those that vanish on
1513:gives the space of all linear transformations from
1158:between super vector spaces is grade preserving if
4361:
4264:
4218:
4189:
4095:
4039:
4015:
3975:
3868:
3821:
3795:
3750:
3665:
3622:
3594:
3574:
3550:
3499:
3451:
3406:
3298:
3235:
3194:
3122:
3092:
3038:
2969:
2949:
2927:
2907:
2880:
2853:
2787:
2734:
2627:
2518:
2486:
2393:
2353:{\displaystyle (V\oplus W)_{1}=V_{1}\oplus W_{1}.}
2352:
2284:{\displaystyle (V\oplus W)_{0}=V_{0}\oplus W_{0},}
2283:
2201:
2179:
2142:
2122:
2095:
2068:
2037:
2017:
1971:
1800:
1777:
1757:
1737:
1714:
1619:
1588:
1545:
1525:
1494:
1417:
1381:
1338:
1304:
1284:
1264:
1244:
1222:{\displaystyle f(V_{i})\subset W_{i},\quad i=0,1.}
1221:
1150:
1094:
984:
958:
924:
904:
884:
846:
809:
778:
758:
738:
718:
691:
660:
621:
597:
574:
477:
450:
423:
403:
383:
345:
318:
288:
187:
138:
118:
94:
60:
4401:Supersymmetry for Mathematicians: An Introduction
5009:
892:where the even subspace is spanned by the first
817:. The standard super coordinate space, denoted
4434:
4352:
4265:{\displaystyle \mathbb {K} -\mathrm {SVect} }
3796:{\displaystyle \mathbb {K} -\mathrm {SVect} }
3500:{\displaystyle \mathbb {K} -\mathrm {SVect} }
3452:{\displaystyle \mathbb {K} -\mathrm {SVect} }
3195:{\displaystyle \mathbb {K} -\mathrm {SVect} }
3093:{\displaystyle \mathbb {K} -\mathrm {SVect} }
361:of a nonzero homogeneous element, denoted by
3108:are super vector spaces (over a fixed field
4394:
4336:
4324:
4312:
4300:
4288:
2977:by considering the (graded) tensor product
1320:homomorphism. The set of all homomorphisms
4441:
4427:
4238:
4212:
4023:can be described as a super vector space
4009:
3769:
3473:
3425:
3215:
3168:
3116:
3066:
2988:
2943:
2812:
2781:
2506:
2381:
2195:
2159:
1105:
866:
826:
279:
266:
252:
175:
88:
48:
195:-graded vector space with decomposition
1765:can be regarded as a homomorphism from
14:
5010:
3039:{\displaystyle \mathbb {K} \otimes V.}
1725:A grade-reversing transformation from
1232:That is, it maps the even elements of
4422:
3558:, given by the super vector space of
2130:to be the space of linear maps from
299:Vectors that are elements of either
3869:{\displaystyle \mathrm {Hom} (V,-)}
3666:{\displaystyle \mathrm {Hom} (V,W)}
3551:{\displaystyle \mathbf {Hom} (V,W)}
3050:The category of super vector spaces
1589:{\displaystyle \mathbf {Hom} (V,W)}
1509:and the grade-reversing ones to be
1382:{\displaystyle \mathrm {Hom} (V,W)}
24:
4258:
4255:
4252:
4249:
4246:
4182:
4085:
4075:
4065:
4032:
3928:
3925:
3922:
3893:
3890:
3887:
3847:
3844:
3841:
3789:
3786:
3783:
3780:
3777:
3690:
3687:
3684:
3644:
3641:
3638:
3616:
3613:
3610:
3493:
3490:
3487:
3484:
3481:
3445:
3442:
3439:
3436:
3433:
3236:{\displaystyle \mathbb {K} ^{1|0}}
3188:
3185:
3182:
3179:
3176:
3086:
3083:
3080:
3077:
3074:
2180:{\displaystyle \mathbb {K} ^{1|0}}
1951:
1944:
1941:
1938:
1915:
1912:
1909:
1896:
1883:
1880:
1877:
1854:
1851:
1848:
1792:
1690:
1687:
1684:
1613:
1610:
1607:
1360:
1357:
1354:
1052:
1009:
976:
885:{\displaystyle \mathbb {K} ^{p+q}}
847:{\displaystyle \mathbb {K} ^{p|q}}
25:
5034:
4448:
3803:is closed means that the functor
2957:can be embedded in a module over
2363:
1983:Operations on super vector spaces
4474:Supersymmetric quantum mechanics
3948:
3945:
3942:
3719:
3716:
3713:
3529:
3526:
3523:
2519:{\displaystyle \mathbb {Z} _{2}}
2394:{\displaystyle \mathbb {Z} _{2}}
1825:
1822:
1819:
1650:
1647:
1644:
1567:
1564:
1561:
1418:{\displaystyle f:V\rightarrow W}
1151:{\displaystyle f:V\rightarrow W}
188:{\displaystyle \mathbb {Z} _{2}}
61:{\displaystyle \mathbb {Z} _{2}}
4167:
3986:
3417:on homogeneous elements, turns
3056:category of super vector spaces
2745:
2103:. Equivalently, one can define
1476:
1203:
237:
4330:
4318:
4306:
4294:
4282:
4204:associative superalgebra over
4160:
4152:
4144:
4136:
4128:
4117:
4080:
4040:{\displaystyle {\mathcal {A}}}
3967:
3964:
3952:
3932:
3915:
3897:
3863:
3851:
3736:
3723:
3706:
3694:
3673:is the even subspace therein:
3660:
3648:
3623:{\displaystyle \mathrm {Hom} }
3545:
3533:
3389:
3381:
3376:
3368:
3363:
3353:
3347:
3335:
3281:
3224:
3024:
2992:
2854:{\displaystyle R=\mathbb {K} }
2848:
2816:
2726:
2700:
2694:
2668:
2656:
2643:
2619:
2593:
2587:
2561:
2549:
2536:
2424:
2411:
2312:
2299:
2243:
2230:
2168:
1963:
1948:
1931:
1919:
1902:
1887:
1870:
1858:
1841:
1829:
1706:
1694:
1666:
1654:
1620:{\displaystyle \mathrm {Hom} }
1583:
1571:
1451:
1438:
1409:
1376:
1364:
1339:{\displaystyle V\rightarrow W}
1330:
1184:
1171:
1142:
1059:
1049:
1016:
1006:
835:
800:
504:
496:
431:according to whether it is in
377:
369:
161:
13:
1:
5023:Categories in category theory
4372:American Mathematical Society
4346:
2864:denote the Grassmann algebra
2212:
1990:
1785:to the parity reversed space
939:of a super vector space is a
4219:{\displaystyle \mathbb {K} }
4016:{\displaystyle \mathbb {K} }
3876:, given a natural bijection
3123:{\displaystyle \mathbb {K} }
2950:{\displaystyle \mathbb {K} }
2788:{\displaystyle \mathbb {K} }
2202:{\displaystyle \mathbb {K} }
1316:of super vector spaces is a
95:{\displaystyle \mathbb {K} }
7:
4469:Supersymmetric gauge theory
3461:symmetric monoidal category
2908:{\displaystyle \theta _{i}}
2888:anticommuting odd elements
2049:to be those that vanish on
946:For any super vector space
10:
5039:
4768:Pure 4D N = 1 supergravity
4047:with a multiplication map
3990:
3822:{\displaystyle -\otimes V}
1126:. A linear transformation
166:A super vector space is a
4899:
4816:
4758:
4702:
4676:
4668:Electricâmagnetic duality
4565:
4502:
4456:
2497:where the indices are in
4689:HaagâĆopuszaĆskiâSohnius
4663:Little hierarchy problem
4275:
3509:closed monoidal category
2764:supercommutative algebra
2526:. Specifically, one has
2025:of a super vector space
4745:6D (2,0) superconformal
2368:One can also construct
641:, and the odd elements
4725:N = 4 super YangâMills
4715:N = 1 super YangâMills
4623:Supersymmetry breaking
4527:Superconformal algebra
4522:Super-Poincaré algebra
4266:
4220:
4191:
4097:
4041:
4017:
3977:
3870:
3823:
3797:
3752:
3667:
3624:
3596:
3576:
3552:
3501:
3453:
3408:
3300:
3237:
3196:
3124:
3094:
3040:
2971:
2951:
2929:
2909:
2882:
2855:
2789:
2736:
2629:
2520:
2488:
2395:
2354:
2285:
2203:
2181:
2144:
2124:
2097:
2070:
2039:
2019:
1973:
1802:
1779:
1759:
1739:
1716:
1621:
1590:
1547:
1527:
1496:
1419:
1383:
1340:
1306:
1286:
1266:
1246:
1223:
1152:
1106:Linear transformations
1096:
986:
960:
926:
906:
886:
848:
811:
780:
760:
740:
720:
693:
672:and the dimensions of
662:
623:
599:
576:
479:
452:
425:
405:
385:
347:
320:
290:
189:
140:
120:
106:of subspaces of grade
96:
62:
4803:Type IIB supergravity
4798:Type IIA supergravity
4773:4D N = 1 supergravity
4638:SeibergâWitten theory
4552:Super Minkowski space
4532:Supersymmetry algebra
4267:
4221:
4192:
4098:
4042:
4018:
3978:
3871:
3824:
3798:
3753:
3668:
3625:
3597:
3577:
3553:
3502:
3454:
3409:
3301:
3238:
3197:
3125:
3095:
3041:
2972:
2952:
2930:
2910:
2883:
2856:
2790:
2737:
2630:
2521:
2489:
2396:
2355:
2286:
2204:
2182:
2145:
2125:
2123:{\displaystyle V^{*}}
2098:
2096:{\displaystyle V_{0}}
2071:
2069:{\displaystyle V_{1}}
2040:
2020:
2018:{\displaystyle V^{*}}
1974:
1803:
1801:{\displaystyle \Pi W}
1780:
1760:
1740:
1717:
1622:
1591:
1548:
1528:
1497:
1420:
1384:
1341:
1307:
1287:
1267:
1247:
1224:
1153:
1124:linear transformation
1097:
987:
985:{\displaystyle \Pi V}
968:parity reversed space
966:, one can define the
961:
927:
907:
887:
849:
812:
781:
761:
741:
721:
719:{\displaystyle V_{1}}
694:
692:{\displaystyle V_{0}}
663:
624:
600:
577:
480:
478:{\displaystyle V_{1}}
453:
451:{\displaystyle V_{0}}
426:
406:
386:
348:
346:{\displaystyle V_{1}}
321:
319:{\displaystyle V_{0}}
291:
190:
141:
121:
97:
63:
5018:Super linear algebra
4588:Short supermultiplet
4234:
4208:
4113:
4054:
4027:
4005:
3883:
3837:
3807:
3765:
3680:
3634:
3606:
3586:
3566:
3519:
3469:
3421:
3316:
3250:
3210:
3164:
3112:
3062:
2984:
2961:
2939:
2919:
2892:
2872:
2802:
2777:
2640:
2533:
2501:
2408:
2376:
2296:
2227:
2191:
2154:
2134:
2107:
2080:
2053:
2029:
2002:
1815:
1789:
1769:
1749:
1729:
1634:
1603:
1557:
1537:
1517:
1432:
1397:
1350:
1324:
1296:
1276:
1272:and odd elements of
1256:
1252:to even elements of
1236:
1165:
1130:
999:
973:
950:
937:homogeneous subspace
916:
896:
861:
821:
793:
770:
750:
730:
703:
676:
652:
613:
609:and those of parity
589:
492:
462:
435:
415:
395:
365:
330:
303:
202:
170:
148:super linear algebra
130:
110:
84:
43:
18:Super linear algebra
4808:Gauged supergravity
4793:Type I supergravity
4750:ABJM superconformal
4547:Harmonic superspace
3513:internal Hom object
2915:. Any super vector
1292:to odd elements of
810:{\displaystyle p|q}
766:respectively, then
384:{\displaystyle |x|}
152:theoretical physics
71:graded vector space
4783:Higher dimensional
4778:N = 8 supergravity
4694:Nonrenormalization
4489:Super vector space
4484:Superstring theory
4396:Varadarajan, V. S.
4374:. pp. 41â97.
4262:
4216:
4187:
4093:
4037:
4013:
3973:
3866:
3819:
3793:
3748:
3663:
3620:
3592:
3572:
3548:
3497:
3449:
3404:
3296:
3233:
3192:
3120:
3090:
3036:
2967:
2947:
2925:
2905:
2878:
2851:
2785:
2732:
2625:
2516:
2484:
2457:
2391:
2350:
2281:
2199:
2177:
2140:
2120:
2093:
2066:
2035:
2015:
1969:
1798:
1775:
1755:
1735:
1712:
1617:
1586:
1543:
1523:
1492:
1415:
1379:
1336:
1302:
1282:
1262:
1242:
1219:
1148:
1092:
1090:
982:
956:
922:
902:
882:
854:, is the ordinary
844:
807:
776:
756:
736:
716:
689:
670:finite-dimensional
658:
619:
595:
585:Vectors of parity
572:
567:
475:
448:
421:
401:
381:
343:
316:
286:
185:
136:
116:
92:
58:
36:super vector space
5005:
5004:
4648:WessâZumino gauge
4411:978-0-8218-3574-6
3595:{\displaystyle W}
3575:{\displaystyle V}
3562:linear maps from
3204:monoidal category
3151:Lie superalgebras
2970:{\displaystyle R}
2928:{\displaystyle V}
2881:{\displaystyle N}
2771:Grassmann algebra
2436:
2143:{\displaystyle V}
2038:{\displaystyle V}
1778:{\displaystyle V}
1758:{\displaystyle W}
1738:{\displaystyle V}
1546:{\displaystyle W}
1526:{\displaystyle V}
1305:{\displaystyle W}
1285:{\displaystyle V}
1265:{\displaystyle W}
1245:{\displaystyle V}
959:{\displaystyle V}
925:{\displaystyle q}
905:{\displaystyle p}
779:{\displaystyle V}
759:{\displaystyle q}
739:{\displaystyle p}
661:{\displaystyle V}
622:{\displaystyle 1}
598:{\displaystyle 0}
424:{\displaystyle 1}
404:{\displaystyle 0}
139:{\displaystyle 1}
119:{\displaystyle 0}
16:(Redirected from
5030:
4788:11D supergravity
4517:Lie superalgebra
4504:Supermathematics
4443:
4436:
4429:
4420:
4419:
4415:
4389:
4365:
4340:
4337:Varadarajan 2004
4334:
4328:
4325:Varadarajan 2004
4322:
4316:
4313:Varadarajan 2004
4310:
4304:
4301:Varadarajan 2004
4298:
4292:
4289:Varadarajan 2004
4286:
4271:
4269:
4268:
4263:
4261:
4241:
4230:in the category
4225:
4223:
4222:
4217:
4215:
4196:
4194:
4193:
4188:
4186:
4185:
4163:
4155:
4147:
4139:
4131:
4120:
4102:
4100:
4099:
4094:
4089:
4088:
4079:
4078:
4069:
4068:
4046:
4044:
4043:
4038:
4036:
4035:
4022:
4020:
4019:
4014:
4012:
3982:
3980:
3979:
3974:
3951:
3931:
3896:
3875:
3873:
3872:
3867:
3850:
3828:
3826:
3825:
3820:
3802:
3800:
3799:
3794:
3792:
3772:
3757:
3755:
3754:
3749:
3744:
3743:
3722:
3693:
3672:
3670:
3669:
3664:
3647:
3629:
3627:
3626:
3621:
3619:
3601:
3599:
3598:
3593:
3581:
3579:
3578:
3573:
3557:
3555:
3554:
3549:
3532:
3506:
3504:
3503:
3498:
3496:
3476:
3458:
3456:
3455:
3450:
3448:
3428:
3413:
3411:
3410:
3405:
3394:
3393:
3392:
3384:
3379:
3371:
3334:
3333:
3305:
3303:
3302:
3297:
3268:
3267:
3242:
3240:
3239:
3234:
3232:
3231:
3227:
3218:
3201:
3199:
3198:
3193:
3191:
3171:
3129:
3127:
3126:
3121:
3119:
3099:
3097:
3096:
3091:
3089:
3069:
3045:
3043:
3042:
3037:
3023:
3022:
3004:
3003:
2991:
2976:
2974:
2973:
2968:
2956:
2954:
2953:
2948:
2946:
2934:
2932:
2931:
2926:
2914:
2912:
2911:
2906:
2904:
2903:
2887:
2885:
2884:
2879:
2860:
2858:
2857:
2852:
2847:
2846:
2828:
2827:
2815:
2794:
2792:
2791:
2786:
2784:
2773:. Given a field
2756:commutative ring
2741:
2739:
2738:
2733:
2725:
2724:
2712:
2711:
2693:
2692:
2680:
2679:
2664:
2663:
2634:
2632:
2631:
2626:
2618:
2617:
2605:
2604:
2586:
2585:
2573:
2572:
2557:
2556:
2525:
2523:
2522:
2517:
2515:
2514:
2509:
2493:
2491:
2490:
2485:
2480:
2479:
2467:
2466:
2456:
2432:
2431:
2400:
2398:
2397:
2392:
2390:
2389:
2384:
2359:
2357:
2356:
2351:
2346:
2345:
2333:
2332:
2320:
2319:
2290:
2288:
2287:
2282:
2277:
2276:
2264:
2263:
2251:
2250:
2208:
2206:
2205:
2200:
2198:
2187:(the base field
2186:
2184:
2183:
2178:
2176:
2175:
2171:
2162:
2149:
2147:
2146:
2141:
2129:
2127:
2126:
2121:
2119:
2118:
2102:
2100:
2099:
2094:
2092:
2091:
2075:
2073:
2072:
2067:
2065:
2064:
2044:
2042:
2041:
2036:
2024:
2022:
2021:
2016:
2014:
2013:
1978:
1976:
1975:
1970:
1947:
1918:
1886:
1857:
1828:
1807:
1805:
1804:
1799:
1784:
1782:
1781:
1776:
1764:
1762:
1761:
1756:
1744:
1742:
1741:
1736:
1721:
1719:
1718:
1713:
1693:
1679:
1678:
1673:
1669:
1653:
1626:
1624:
1623:
1618:
1616:
1595:
1593:
1592:
1587:
1570:
1552:
1550:
1549:
1544:
1532:
1530:
1529:
1524:
1501:
1499:
1498:
1493:
1472:
1471:
1450:
1449:
1424:
1422:
1421:
1416:
1388:
1386:
1385:
1380:
1363:
1345:
1343:
1342:
1337:
1311:
1309:
1308:
1303:
1291:
1289:
1288:
1283:
1271:
1269:
1268:
1263:
1251:
1249:
1248:
1243:
1228:
1226:
1225:
1220:
1199:
1198:
1183:
1182:
1157:
1155:
1154:
1149:
1101:
1099:
1098:
1093:
1091:
1084:
1083:
1067:
1066:
1041:
1040:
1024:
1023:
991:
989:
988:
983:
965:
963:
962:
957:
931:
929:
928:
923:
911:
909:
908:
903:
891:
889:
888:
883:
881:
880:
869:
856:coordinate space
853:
851:
850:
845:
843:
842:
838:
829:
816:
814:
813:
808:
803:
786:is said to have
785:
783:
782:
777:
765:
763:
762:
757:
745:
743:
742:
737:
725:
723:
722:
717:
715:
714:
698:
696:
695:
690:
688:
687:
667:
665:
664:
659:
628:
626:
625:
620:
604:
602:
601:
596:
581:
579:
578:
573:
571:
570:
564:
563:
539:
538:
507:
499:
484:
482:
481:
476:
474:
473:
457:
455:
454:
449:
447:
446:
430:
428:
427:
422:
410:
408:
407:
402:
390:
388:
387:
382:
380:
372:
352:
350:
349:
344:
342:
341:
325:
323:
322:
317:
315:
314:
295:
293:
292:
287:
282:
274:
269:
261:
260:
255:
233:
232:
220:
219:
194:
192:
191:
186:
184:
183:
178:
145:
143:
142:
137:
125:
123:
122:
117:
101:
99:
98:
93:
91:
67:
65:
64:
59:
57:
56:
51:
21:
5038:
5037:
5033:
5032:
5031:
5029:
5028:
5027:
5008:
5007:
5006:
5001:
4895:
4812:
4754:
4698:
4684:ColemanâMandula
4672:
4633:Seiberg duality
4628:Konishi anomaly
4561:
4498:
4452:
4447:
4412:
4382:
4370:. Vol. 1.
4349:
4344:
4343:
4335:
4331:
4323:
4319:
4311:
4307:
4299:
4295:
4287:
4283:
4278:
4245:
4237:
4235:
4232:
4231:
4211:
4209:
4206:
4205:
4181:
4180:
4159:
4151:
4143:
4135:
4127:
4116:
4114:
4111:
4110:
4084:
4083:
4074:
4073:
4064:
4063:
4055:
4052:
4051:
4031:
4030:
4028:
4025:
4024:
4008:
4006:
4003:
4002:
3995:
3989:
3941:
3921:
3886:
3884:
3881:
3880:
3840:
3838:
3835:
3834:
3833:to the functor
3808:
3805:
3804:
3776:
3768:
3766:
3763:
3762:
3739:
3735:
3712:
3683:
3681:
3678:
3677:
3637:
3635:
3632:
3631:
3609:
3607:
3604:
3603:
3602:. The ordinary
3587:
3584:
3583:
3567:
3564:
3563:
3522:
3520:
3517:
3516:
3480:
3472:
3470:
3467:
3466:
3432:
3424:
3422:
3419:
3418:
3388:
3380:
3375:
3367:
3366:
3362:
3323:
3319:
3317:
3314:
3313:
3257:
3253:
3251:
3248:
3247:
3223:
3219:
3214:
3213:
3211:
3208:
3207:
3175:
3167:
3165:
3162:
3161:
3143:category theory
3115:
3113:
3110:
3109:
3073:
3065:
3063:
3060:
3059:
3052:
3018:
3014:
2999:
2995:
2987:
2985:
2982:
2981:
2962:
2959:
2958:
2942:
2940:
2937:
2936:
2920:
2917:
2916:
2899:
2895:
2893:
2890:
2889:
2873:
2870:
2869:
2842:
2838:
2823:
2819:
2811:
2803:
2800:
2799:
2780:
2778:
2775:
2774:
2748:
2720:
2716:
2707:
2703:
2688:
2684:
2675:
2671:
2659:
2655:
2641:
2638:
2637:
2613:
2609:
2600:
2596:
2581:
2577:
2568:
2564:
2552:
2548:
2534:
2531:
2530:
2510:
2505:
2504:
2502:
2499:
2498:
2475:
2471:
2462:
2458:
2440:
2427:
2423:
2409:
2406:
2405:
2385:
2380:
2379:
2377:
2374:
2373:
2370:tensor products
2366:
2341:
2337:
2328:
2324:
2315:
2311:
2297:
2294:
2293:
2272:
2268:
2259:
2255:
2246:
2242:
2228:
2225:
2224:
2215:
2194:
2192:
2189:
2188:
2167:
2163:
2158:
2157:
2155:
2152:
2151:
2135:
2132:
2131:
2114:
2110:
2108:
2105:
2104:
2087:
2083:
2081:
2078:
2077:
2060:
2056:
2054:
2051:
2050:
2030:
2027:
2026:
2009:
2005:
2003:
2000:
1999:
1993:
1985:
1937:
1908:
1876:
1847:
1818:
1816:
1813:
1812:
1790:
1787:
1786:
1770:
1767:
1766:
1750:
1747:
1746:
1730:
1727:
1726:
1683:
1674:
1643:
1642:
1638:
1637:
1635:
1632:
1631:
1606:
1604:
1601:
1600:
1560:
1558:
1555:
1554:
1538:
1535:
1534:
1518:
1515:
1514:
1461:
1457:
1445:
1441:
1433:
1430:
1429:
1398:
1395:
1394:
1353:
1351:
1348:
1347:
1325:
1322:
1321:
1297:
1294:
1293:
1277:
1274:
1273:
1257:
1254:
1253:
1237:
1234:
1233:
1194:
1190:
1178:
1174:
1166:
1163:
1162:
1131:
1128:
1127:
1108:
1089:
1088:
1079:
1075:
1068:
1062:
1058:
1046:
1045:
1036:
1032:
1025:
1019:
1015:
1002:
1000:
997:
996:
974:
971:
970:
951:
948:
947:
941:linear subspace
917:
914:
913:
897:
894:
893:
870:
865:
864:
862:
859:
858:
834:
830:
825:
824:
822:
819:
818:
799:
794:
791:
790:
771:
768:
767:
751:
748:
747:
731:
728:
727:
710:
706:
704:
701:
700:
683:
679:
677:
674:
673:
653:
650:
649:
614:
611:
610:
590:
587:
586:
566:
565:
559:
555:
547:
541:
540:
534:
530:
522:
512:
511:
503:
495:
493:
490:
489:
469:
465:
463:
460:
459:
442:
438:
436:
433:
432:
416:
413:
412:
396:
393:
392:
376:
368:
366:
363:
362:
353:are said to be
337:
333:
331:
328:
327:
310:
306:
304:
301:
300:
278:
270:
265:
256:
251:
250:
228:
224:
215:
211:
203:
200:
199:
179:
174:
173:
171:
168:
167:
164:
131:
128:
127:
111:
108:
107:
87:
85:
82:
81:
52:
47:
46:
44:
41:
40:
28:
23:
22:
15:
12:
11:
5:
5036:
5026:
5025:
5020:
5003:
5002:
5000:
4999:
4994:
4989:
4984:
4979:
4974:
4969:
4964:
4959:
4954:
4949:
4944:
4939:
4934:
4929:
4924:
4919:
4914:
4909:
4903:
4901:
4897:
4896:
4894:
4893:
4888:
4883:
4878:
4873:
4868:
4863:
4858:
4853:
4848:
4843:
4838:
4833:
4828:
4822:
4820:
4814:
4813:
4811:
4810:
4805:
4800:
4795:
4790:
4785:
4780:
4775:
4770:
4764:
4762:
4756:
4755:
4753:
4752:
4747:
4742:
4737:
4732:
4727:
4722:
4717:
4712:
4706:
4704:
4703:Field theories
4700:
4699:
4697:
4696:
4691:
4686:
4680:
4678:
4674:
4673:
4671:
4670:
4665:
4660:
4655:
4650:
4645:
4640:
4635:
4630:
4625:
4620:
4615:
4610:
4605:
4600:
4598:Superpotential
4595:
4590:
4585:
4583:Supermultiplet
4580:
4575:
4569:
4567:
4563:
4562:
4560:
4559:
4554:
4549:
4544:
4539:
4534:
4529:
4524:
4519:
4514:
4508:
4506:
4500:
4499:
4497:
4496:
4491:
4486:
4481:
4476:
4471:
4466:
4460:
4458:
4457:General topics
4454:
4453:
4446:
4445:
4438:
4431:
4423:
4417:
4416:
4410:
4391:
4390:
4380:
4348:
4345:
4342:
4341:
4329:
4317:
4305:
4293:
4280:
4279:
4277:
4274:
4260:
4257:
4254:
4251:
4248:
4244:
4240:
4214:
4198:
4197:
4184:
4179:
4176:
4173:
4170:
4166:
4162:
4158:
4154:
4150:
4146:
4142:
4138:
4134:
4130:
4126:
4123:
4119:
4104:
4103:
4092:
4087:
4082:
4077:
4072:
4067:
4062:
4059:
4034:
4011:
3991:Main article:
3988:
3985:
3984:
3983:
3972:
3969:
3966:
3963:
3960:
3957:
3954:
3950:
3947:
3944:
3940:
3937:
3934:
3930:
3927:
3924:
3920:
3917:
3914:
3911:
3908:
3905:
3902:
3899:
3895:
3892:
3889:
3865:
3862:
3859:
3856:
3853:
3849:
3846:
3843:
3818:
3815:
3812:
3791:
3788:
3785:
3782:
3779:
3775:
3771:
3761:The fact that
3759:
3758:
3747:
3742:
3738:
3734:
3731:
3728:
3725:
3721:
3718:
3715:
3711:
3708:
3705:
3702:
3699:
3696:
3692:
3689:
3686:
3662:
3659:
3656:
3653:
3650:
3646:
3643:
3640:
3618:
3615:
3612:
3591:
3571:
3547:
3544:
3541:
3538:
3535:
3531:
3528:
3525:
3495:
3492:
3489:
3486:
3483:
3479:
3475:
3447:
3444:
3441:
3438:
3435:
3431:
3427:
3415:
3414:
3403:
3400:
3397:
3391:
3387:
3383:
3378:
3374:
3370:
3365:
3361:
3358:
3355:
3352:
3349:
3346:
3343:
3340:
3337:
3332:
3329:
3326:
3322:
3307:
3306:
3295:
3292:
3289:
3286:
3283:
3280:
3277:
3274:
3271:
3266:
3263:
3260:
3256:
3230:
3226:
3222:
3217:
3190:
3187:
3184:
3181:
3178:
3174:
3170:
3118:
3088:
3085:
3082:
3079:
3076:
3072:
3068:
3051:
3048:
3047:
3046:
3035:
3032:
3029:
3026:
3021:
3017:
3013:
3010:
3007:
3002:
2998:
2994:
2990:
2966:
2945:
2924:
2902:
2898:
2877:
2862:
2861:
2850:
2845:
2841:
2837:
2834:
2831:
2826:
2822:
2818:
2814:
2810:
2807:
2783:
2747:
2744:
2743:
2742:
2731:
2728:
2723:
2719:
2715:
2710:
2706:
2702:
2699:
2696:
2691:
2687:
2683:
2678:
2674:
2670:
2667:
2662:
2658:
2654:
2651:
2648:
2645:
2635:
2624:
2621:
2616:
2612:
2608:
2603:
2599:
2595:
2592:
2589:
2584:
2580:
2576:
2571:
2567:
2563:
2560:
2555:
2551:
2547:
2544:
2541:
2538:
2513:
2508:
2495:
2494:
2483:
2478:
2474:
2470:
2465:
2461:
2455:
2452:
2449:
2446:
2443:
2439:
2435:
2430:
2426:
2422:
2419:
2416:
2413:
2388:
2383:
2365:
2364:Tensor product
2362:
2361:
2360:
2349:
2344:
2340:
2336:
2331:
2327:
2323:
2318:
2314:
2310:
2307:
2304:
2301:
2291:
2280:
2275:
2271:
2267:
2262:
2258:
2254:
2249:
2245:
2241:
2238:
2235:
2232:
2214:
2211:
2197:
2174:
2170:
2166:
2161:
2139:
2117:
2113:
2090:
2086:
2063:
2059:
2034:
2012:
2008:
1992:
1989:
1984:
1981:
1980:
1979:
1968:
1965:
1962:
1959:
1956:
1953:
1950:
1946:
1943:
1940:
1936:
1933:
1930:
1927:
1924:
1921:
1917:
1914:
1911:
1907:
1904:
1901:
1898:
1895:
1892:
1889:
1885:
1882:
1879:
1875:
1872:
1869:
1866:
1863:
1860:
1856:
1853:
1850:
1846:
1843:
1840:
1837:
1834:
1831:
1827:
1824:
1821:
1797:
1794:
1774:
1754:
1734:
1723:
1722:
1711:
1708:
1705:
1702:
1699:
1696:
1692:
1689:
1686:
1682:
1677:
1672:
1668:
1665:
1662:
1659:
1656:
1652:
1649:
1646:
1641:
1615:
1612:
1609:
1585:
1582:
1579:
1576:
1573:
1569:
1566:
1563:
1542:
1522:
1503:
1502:
1491:
1488:
1485:
1482:
1479:
1475:
1470:
1467:
1464:
1460:
1456:
1453:
1448:
1444:
1440:
1437:
1414:
1411:
1408:
1405:
1402:
1378:
1375:
1372:
1369:
1366:
1362:
1359:
1356:
1335:
1332:
1329:
1301:
1281:
1261:
1241:
1230:
1229:
1218:
1215:
1212:
1209:
1206:
1202:
1197:
1193:
1189:
1186:
1181:
1177:
1173:
1170:
1147:
1144:
1141:
1138:
1135:
1107:
1104:
1103:
1102:
1087:
1082:
1078:
1074:
1071:
1069:
1065:
1061:
1057:
1054:
1051:
1048:
1047:
1044:
1039:
1035:
1031:
1028:
1026:
1022:
1018:
1014:
1011:
1008:
1005:
1004:
981:
978:
955:
921:
901:
879:
876:
873:
868:
841:
837:
833:
828:
806:
802:
798:
775:
755:
735:
713:
709:
686:
682:
657:
643:Fermi elements
618:
594:
583:
582:
569:
562:
558:
554:
551:
548:
546:
543:
542:
537:
533:
529:
526:
523:
521:
518:
517:
515:
510:
506:
502:
498:
472:
468:
445:
441:
420:
400:
379:
375:
371:
340:
336:
313:
309:
297:
296:
285:
281:
277:
273:
268:
264:
259:
254:
249:
246:
243:
240:
236:
231:
227:
223:
218:
214:
210:
207:
182:
177:
163:
160:
135:
115:
90:
55:
50:
26:
9:
6:
4:
3:
2:
5035:
5024:
5021:
5019:
5016:
5015:
5013:
4998:
4995:
4993:
4990:
4988:
4985:
4983:
4980:
4978:
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4958:
4955:
4953:
4950:
4948:
4945:
4943:
4940:
4938:
4935:
4933:
4930:
4928:
4925:
4923:
4920:
4918:
4915:
4913:
4910:
4908:
4905:
4904:
4902:
4898:
4892:
4889:
4887:
4884:
4882:
4879:
4877:
4874:
4872:
4869:
4867:
4864:
4862:
4859:
4857:
4854:
4852:
4849:
4847:
4844:
4842:
4839:
4837:
4834:
4832:
4829:
4827:
4824:
4823:
4821:
4819:
4818:Superpartners
4815:
4809:
4806:
4804:
4801:
4799:
4796:
4794:
4791:
4789:
4786:
4784:
4781:
4779:
4776:
4774:
4771:
4769:
4766:
4765:
4763:
4761:
4757:
4751:
4748:
4746:
4743:
4741:
4738:
4736:
4733:
4731:
4728:
4726:
4723:
4721:
4718:
4716:
4713:
4711:
4708:
4707:
4705:
4701:
4695:
4692:
4690:
4687:
4685:
4682:
4681:
4679:
4675:
4669:
4666:
4664:
4661:
4659:
4656:
4654:
4651:
4649:
4646:
4644:
4641:
4639:
4636:
4634:
4631:
4629:
4626:
4624:
4621:
4619:
4616:
4614:
4611:
4609:
4606:
4604:
4601:
4599:
4596:
4594:
4591:
4589:
4586:
4584:
4581:
4579:
4576:
4574:
4571:
4570:
4568:
4564:
4558:
4557:Supermanifold
4555:
4553:
4550:
4548:
4545:
4543:
4540:
4538:
4535:
4533:
4530:
4528:
4525:
4523:
4520:
4518:
4515:
4513:
4510:
4509:
4507:
4505:
4501:
4495:
4494:Supergeometry
4492:
4490:
4487:
4485:
4482:
4480:
4477:
4475:
4472:
4470:
4467:
4465:
4464:Supersymmetry
4462:
4461:
4459:
4455:
4451:
4450:Supersymmetry
4444:
4439:
4437:
4432:
4430:
4425:
4424:
4421:
4413:
4407:
4403:
4402:
4397:
4393:
4392:
4387:
4383:
4381:0-8218-2012-5
4377:
4373:
4369:
4364:
4359:
4358:Morgan, J. W.
4355:
4351:
4350:
4338:
4333:
4326:
4321:
4314:
4309:
4302:
4297:
4290:
4285:
4281:
4273:
4242:
4229:
4203:
4177:
4174:
4171:
4168:
4164:
4156:
4148:
4140:
4132:
4124:
4121:
4109:
4108:
4107:
4090:
4070:
4060:
4057:
4050:
4049:
4048:
4000:
3994:
3970:
3961:
3958:
3955:
3938:
3935:
3918:
3912:
3909:
3906:
3903:
3900:
3879:
3878:
3877:
3860:
3857:
3854:
3832:
3816:
3813:
3810:
3773:
3745:
3740:
3732:
3729:
3726:
3709:
3703:
3700:
3697:
3676:
3675:
3674:
3657:
3654:
3651:
3589:
3569:
3561:
3542:
3539:
3536:
3514:
3510:
3477:
3464:
3462:
3429:
3401:
3398:
3395:
3385:
3372:
3359:
3356:
3350:
3344:
3341:
3338:
3330:
3327:
3324:
3320:
3312:
3311:
3310:
3293:
3290:
3287:
3284:
3278:
3275:
3272:
3269:
3264:
3261:
3258:
3254:
3246:
3245:
3244:
3228:
3220:
3205:
3172:
3160:The category
3158:
3156:
3152:
3148:
3147:superalgebras
3144:
3139:
3137:
3133:
3107:
3103:
3070:
3058:, denoted by
3057:
3033:
3030:
3027:
3019:
3015:
3011:
3008:
3005:
3000:
2996:
2980:
2979:
2978:
2964:
2922:
2900:
2896:
2875:
2867:
2843:
2839:
2835:
2832:
2829:
2824:
2820:
2808:
2805:
2798:
2797:
2796:
2772:
2767:
2765:
2761:
2757:
2753:
2729:
2721:
2717:
2713:
2708:
2704:
2697:
2689:
2685:
2681:
2676:
2672:
2665:
2660:
2652:
2649:
2646:
2636:
2622:
2614:
2610:
2606:
2601:
2597:
2590:
2582:
2578:
2574:
2569:
2565:
2558:
2553:
2545:
2542:
2539:
2529:
2528:
2527:
2511:
2481:
2476:
2472:
2468:
2463:
2459:
2453:
2450:
2447:
2444:
2441:
2437:
2433:
2428:
2420:
2417:
2414:
2404:
2403:
2402:
2386:
2371:
2347:
2342:
2338:
2334:
2329:
2325:
2321:
2316:
2308:
2305:
2302:
2292:
2278:
2273:
2269:
2265:
2260:
2256:
2252:
2247:
2239:
2236:
2233:
2223:
2222:
2221:
2219:
2210:
2172:
2164:
2137:
2115:
2111:
2088:
2084:
2061:
2057:
2048:
2032:
2010:
2006:
1998:
1988:
1966:
1960:
1957:
1954:
1934:
1928:
1925:
1922:
1905:
1899:
1893:
1890:
1873:
1867:
1864:
1861:
1844:
1838:
1835:
1832:
1811:
1810:
1809:
1795:
1772:
1752:
1732:
1709:
1703:
1700:
1697:
1680:
1675:
1670:
1663:
1660:
1657:
1639:
1630:
1629:
1628:
1599:
1580:
1577:
1574:
1540:
1520:
1512:
1508:
1489:
1486:
1483:
1480:
1477:
1473:
1468:
1465:
1462:
1458:
1454:
1446:
1442:
1435:
1428:
1427:
1426:
1412:
1406:
1403:
1400:
1390:
1373:
1370:
1367:
1333:
1327:
1319:
1315:
1299:
1279:
1259:
1239:
1216:
1213:
1210:
1207:
1204:
1200:
1195:
1191:
1187:
1179:
1175:
1168:
1161:
1160:
1159:
1145:
1139:
1136:
1133:
1125:
1121:
1117:
1113:
1085:
1080:
1076:
1072:
1070:
1063:
1055:
1042:
1037:
1033:
1029:
1027:
1020:
1012:
995:
994:
993:
979:
969:
953:
944:
942:
938:
933:
919:
899:
877:
874:
871:
857:
839:
831:
804:
796:
789:
773:
753:
733:
711:
707:
684:
680:
671:
655:
646:
644:
640:
636:
635:Bose elements
632:
616:
608:
592:
560:
556:
552:
549:
544:
535:
531:
527:
524:
519:
513:
508:
500:
488:
487:
486:
470:
466:
443:
439:
418:
398:
373:
360:
356:
338:
334:
311:
307:
283:
275:
271:
262:
257:
247:
244:
241:
238:
234:
229:
225:
221:
216:
212:
208:
205:
198:
197:
196:
180:
159:
157:
156:supersymmetry
153:
149:
133:
113:
105:
104:decomposition
102:with a given
80:
76:
73:, that is, a
72:
68:
53:
37:
33:
19:
4760:Supergravity
4653:Localization
4643:Witten index
4618:Moduli space
4512:Superalgebra
4488:
4479:Supergravity
4400:
4384:– via
4367:
4339:, p. 87
4332:
4327:, p. 84
4320:
4315:, p. 83
4308:
4303:, p. 83
4296:
4291:, p. 83
4284:
4199:
4105:
3999:superalgebra
3996:
3993:superalgebra
3987:Superalgebra
3831:left adjoint
3760:
3559:
3465:
3416:
3308:
3159:
3140:
3135:
3130:) and whose
3055:
3053:
2863:
2768:
2760:supermodules
2749:
2746:Supermodules
2496:
2367:
2216:
1994:
1986:
1724:
1597:
1510:
1506:
1504:
1391:
1231:
1112:homomorphism
1109:
967:
945:
936:
934:
787:
647:
642:
638:
634:
630:
606:
584:
358:
354:
298:
165:
147:
75:vector space
35:
29:
4900:Researchers
4886:Stop squark
4851:Graviscalar
4846:Graviphoton
4710:WessâZumino
4573:Supercharge
4354:Deligne, P.
3155:supergroups
2935:space over
2766:(or ring).
2218:Direct sums
2047:functionals
1596:and called
1425:such that
1346:is denoted
1314:isomorphism
629:are called
605:are called
355:homogeneous
162:Definitions
32:mathematics
5012:Categories
4947:Iliopoulos
4891:Superghost
4881:Sgoldstino
4866:Neutralino
4658:Mu problem
4578:R-symmetry
4542:Superspace
4537:Supergroup
4347:References
3507:is also a
2213:Direct sum
1997:dual space
1991:Dual space
1808:, so that
1553:, denoted
126:and grade
4917:Batchelor
4841:Goldstino
4730:Super QCD
4608:FI D-term
4593:BPS state
4243:−
4178:∈
4081:→
4071:⊗
4058:μ
3919:≅
3904:⊗
3861:−
3814:⊗
3811:−
3774:−
3511:with the
3478:−
3430:−
3399:⊗
3357:−
3342:⊗
3321:τ
3309:given by
3288:⊗
3282:→
3276:⊗
3255:τ
3173:−
3132:morphisms
3100:, is the
3071:−
3028:⊗
3016:θ
3009:⋯
2997:θ
2897:θ
2866:generated
2840:θ
2833:⋯
2821:θ
2714:⊗
2698:⊕
2682:⊗
2650:⊗
2607:⊗
2591:⊕
2575:⊗
2543:⊗
2469:⊗
2438:⨁
2418:⊗
2335:⊕
2306:⊕
2266:⊕
2237:⊕
2116:∗
2011:∗
1952:Π
1935:⊕
1897:Π
1874:⊕
1793:Π
1466:−
1455:⊂
1410:→
1331:→
1318:bijective
1188:⊂
1143:→
1053:Π
1010:Π
977:Π
788:dimension
553:∈
528:∈
248:∈
222:⊕
4952:Montonen
4876:Sfermion
4871:R-hadron
4856:Higgsino
4831:Chargino
4720:4D N = 1
4677:Theorems
4566:Concepts
4398:(2004).
4360:(1999).
3102:category
1598:internal
1120:category
1116:morphism
4967:Seiberg
4942:Golfand
4922:Berezin
4907:Affleck
4836:Gaugino
3459:into a
3106:objects
2762:over a
2754:over a
2752:modules
1118:in the
639:bosonic
77:over a
4997:Zumino
4992:Witten
4982:Rogers
4972:Siegel
4912:Bagger
4613:F-term
4603:D-term
4408:
4378:
4228:monoid
4202:unital
3104:whose
359:parity
357:. The
4977:RoÄek
4962:Salam
4957:Olive
4937:Gates
4932:Fayet
4826:Axino
4740:NMSSM
4276:Notes
4226:is a
4001:over
3202:is a
1312:. An
391:, is
79:field
38:is a
4987:Wess
4927:Dine
4735:MSSM
4406:ISBN
4376:ISBN
3630:set
3136:even
3134:are
3054:The
2795:let
1995:The
1507:even
1114:, a
746:and
726:are
699:and
607:even
34:, a
4861:LSP
4386:IAS
3829:is
3582:to
3560:all
2868:by
2150:to
1745:to
1533:to
1511:odd
668:is
648:If
637:or
631:odd
458:or
411:or
326:or
30:In
5014::
4366:.
4356:;
4272:.
3997:A
3515:,
3153:,
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3034:.
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3025:]
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3012:,
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2993:[
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2813:K
2809:=
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2317:1
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2253:=
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2173:0
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2007:V
1967:.
1964:)
1961:W
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1949:(
1945:m
1942:o
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1929:W
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1923:V
1920:(
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1900:W
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