605:
into even and odd components, then two distinct (but essentially equivalent) sign conventions can be found in the literature. These can be called the "cohomological sign convention" and the "super sign convention". They differ in how the antipode (exchange of two elements) behaves. In the first case,
2265:
3572:
2621:
2294:
One can easily generalize the definition of superalgebras to include superalgebras over a commutative superring. The definition given above is then a specialization to the case where the base ring is purely even.
2029:
2456:
1485:
1119:
1411:
1777:
2278:
is purely even, this is equivalent to the ordinary ungraded tensor product (except that the result is graded). However, in general, the super tensor product is distinct from the tensor product of
2558:
3517:
275:
670:
1658:
1597:
885:
2084:
557:
1890:
197:
3562:
1178:
1147:
960:
924:
464:. The identity element in a unital superalgebra is necessarily even. Unless otherwise specified, all superalgebras in this article are assumed to be associative and unital.
3567:
2808:
443:
962:
the parity. This is more often seen in physics texts, and requires a parity functor to be judiciously employed to track isomorphisms. Detailed arguments are provided by
785:
705:
574:. There are superalgebras that are commutative in the ordinary sense, but not in the superalgebra sense. For this reason, commutative superalgebras are often called
830:
This convention is commonly seen in conventional mathematical settings, such as differential geometry and differential topology. The other convention is to take
828:
2553:
805:
753:
733:
3186:
3555:
3191:
2717:
2801:
3785:
2915:
3633:
3550:
3932:
3881:
86:
1944:
3368:
1042:
together form a superalgebra, being the even and odd parts, respectively. Note that this is a different grading from the grading by degree.
3917:
3907:
2794:
3413:
2342:
3886:
1422:
2920:
2767:
3329:
1058:
1343:
3927:
2930:
2777:
2727:
1694:
3937:
3496:
2950:
2945:
3626:
2751:
2697:
4053:
3942:
3666:
3363:
3047:
1684:(in particular, if 2 is invertible) then the grade involution can be used to distinguish the even and odd parts of
3980:
3975:
3110:
2870:
224:
3912:
3037:
612:
69:, provide an algebraic framework for formulating supersymmetry. The study of such objects is sometimes called
4215:
3619:
3042:
2935:
2260:{\displaystyle (a_{1}\otimes b_{1})(a_{2}\otimes b_{2})=(-1)^{|b_{1}||a_{2}|}(a_{1}a_{2}\otimes b_{1}b_{2}).}
1608:
1538:
3596:
2940:
1239:
836:
54:
with a decomposition into "even" and "odd" pieces and a multiplication operator that respects the grading.
487:
3960:
3876:
3845:
3800:
3661:
2982:
1803:
156:
3860:
3600:
3064:
2059:
3830:
3460:
3393:
3388:
3351:
2882:
2855:
2825:
3714:
1155:
1124:
929:
893:
3855:
3317:
3312:
3221:
3181:
2897:
2532:
1522:
1028:
469:
114:
383:
3506:
1238:. Lie superalgebras are nonunital and nonassociative; however, one may construct the analog of a
1039:
3142:
1004:
may be regarded as superalgebra by reading the grading modulo 2. This includes examples such as
3965:
3815:
3719:
3511:
3501:
3475:
3297:
3292:
3287:
3282:
3240:
3203:
3149:
2875:
2865:
2843:
2512:
1274:, consisting of all even elements, is closed under multiplication and contains the identity of
1216:). This algebra may be identified with the algebra of endomorphisms of a free supermodule over
758:
678:
3995:
3990:
3902:
3840:
3744:
3724:
3428:
3408:
3346:
3275:
3054:
3032:
3007:
2907:
1291:
1035:
147:
43:
3780:
3729:
3586:
3480:
3465:
3380:
3307:
3270:
3265:
3255:
3015:
2969:
2039:
137:
70:
2616:{\displaystyle {\begin{aligned}\mu &:A\otimes A\to A\\\eta &:R\to A\end{aligned}}}
8:
4000:
3985:
3970:
3739:
3455:
3324:
3235:
3122:
3093:
2817:
110:
51:
24:
810:
4109:
3681:
3676:
3592:
3245:
3231:
3213:
3196:
3176:
3159:
3069:
2892:
1185:
790:
738:
718:
281:
2046:
as an ungraded algebra. A commutative superalgebra is one whose supercenter is all of
4210:
3418:
3154:
3132:
3059:
3020:
2997:
2786:
2773:
2772:. Courant Lecture Notes in Mathematics. Vol. 11. American Mathematical Society.
2763:
2747:
2723:
2693:
2520:
1681:
3810:
3709:
3696:
3336:
3127:
3115:
3098:
3076:
3025:
2977:
2838:
1231:
1045:
1020:
461:
102:
47:
2669:
4139:
4104:
3825:
3820:
3442:
3398:
3225:
3169:
3164:
3103:
2925:
2850:
2508:
1789:
1009:
78:
4169:
4159:
4144:
3790:
3775:
3086:
2688:; Morgan, J. W. (1999). "Notes on Supersymmetry (following Joseph Bernstein)".
2685:
1005:
1001:
963:
602:
39:
4204:
4184:
4164:
4114:
3749:
3686:
3656:
3642:
3403:
3358:
3341:
2987:
2860:
2713:
1335:
1192:
474:
82:
74:
62:
4189:
4174:
4134:
4124:
4119:
4010:
3952:
3835:
3671:
3302:
3081:
2992:
2887:
1525:
1052:
203:
4179:
4154:
4149:
4099:
4078:
4043:
4038:
3765:
3534:
3450:
2311:
1235:
473:(or supercommutative algebra) is one which satisfies a graded version of
453:
306:
66:
20:
4083:
4073:
4058:
3850:
3770:
3734:
3470:
2739:
2709:
1279:
2024:{\displaystyle \mathrm {Z} (A)=\{a\in A:=0{\text{ for all }}x\in A\}.}
4129:
4033:
3922:
3518:
The
Unreasonable Effectiveness of Mathematics in the Natural Sciences
2833:
2527:
serving as the unit object. An associative, unital superalgebra over
1265:
1027:
is a superalgebra. The exterior algebra is the standard example of a
4068:
4063:
4048:
4023:
1316:
1242:
of a Lie superalgebra which is a unital, associative superalgebra.
4028:
310:
65:
in theoretical physics. Superalgebras and their representations,
3611:
2451:{\displaystyle r\cdot (xy)=(r\cdot x)y=(-1)^{|r||x|}x(r\cdot y)}
73:. Superalgebras also play an important role in related field of
3805:
3795:
3573:
European
Community on Computational Methods in Applied Sciences
3137:
2955:
1480:{\displaystyle \mu (x\otimes y)\cdot z=x\cdot \mu (y\otimes z)}
2692:. Vol. 1. American Mathematical Society. pp. 41â97.
4018:
2289:
943:
907:
3568:
International
Council for Industrial and Applied Mathematics
2722:. Memoirs of the AMS Series. Vol. 711. AMS Bookstore.
1114:{\displaystyle \mathbf {End} (V)\equiv \mathbf {Hom} (V,V)}
1509:. This follows from the associativity of the product in
1406:{\displaystyle \mu :A_{1}\otimes _{A_{0}}A_{1}\to A_{0}}
1246:
2690:
Quantum Fields and
Strings: A Course for Mathematicians
2336:
that respects the grading. Bilinearity here means that
2816:
1772:{\displaystyle A_{i}=\{x\in A:{\hat {x}}=(-1)^{i}x\}.}
1319:
whose scalar multiplication is just multiplication in
3187:
Numerical methods for ordinary differential equations
2556:
2345:
2087:
1947:
1806:
1697:
1611:
1541:
1425:
1346:
1158:
1127:
1061:
1048:
are superalgebras. They are generally noncommutative.
932:
896:
839:
813:
793:
761:
741:
721:
681:
615:
490:
386:
227:
159:
3563:
Société de Mathématiques
Appliquées et Industrielles
3556:
Japan
Society for Industrial and Applied Mathematics
3192:
Numerical methods for partial differential equations
2906:
3379:
2708:
2641:
978:may be regarded as a purely even superalgebra over
2615:
2450:
2259:
2023:
1884:
1771:
1652:
1591:
1479:
1405:
1172:
1141:
1113:
954:
918:
879:
822:
799:
779:
747:
727:
699:
664:
551:
437:
269:
191:
2769:Supersymmetry for Mathematicians: An Introduction
2484:Equivalently, one may define a superalgebra over
4202:
2719:Graded simple Jordan superalgebras of growth one
1228:and is the internal Hom of above for this space.
346:|, is 0 or 1 according to whether it is in
16:Algebraic structure used in theoretical physics
3551:Society for Industrial and Applied Mathematics
3627:
2802:
2684:
2539:-supermodules. That is, a superalgebra is an
3369:Supersymmetric theory of stochastic dynamics
2015:
1965:
1895:on homogeneous elements, extended to all of
1763:
1711:
376:are both homogeneous then so is the product
2762:
2653:
284:2, i.e. they are thought of as elements of
270:{\displaystyle A_{i}A_{j}\subseteq A_{i+j}}
3634:
3620:
2809:
2795:
2290:Generalizations and categorical definition
2078:with a multiplication rule determined by:
1260:be a superalgebra over a commutative ring
2664:
2662:
2286:regarded as ordinary, ungraded algebras.
1532:. It is given on homogeneous elements by
548:
77:where they enter into the definitions of
2746:((2nd ed.) ed.). Berlin: Springer.
2492:together with an superring homomorphism
1934:which supercommute with all elements of
665:{\displaystyle xy\mapsto (-1)^{mn+pq}yx}
2744:Gauge Field Theory and Complex Geometry
2500:whose image lies in the supercenter of
2053:
1188:forms a superalgebra under composition.
4203:
2659:
2626:for which the usual diagrams commute.
1653:{\displaystyle {\hat {x}}=x_{0}-x_{1}}
1592:{\displaystyle {\hat {x}}=(-1)^{|x|}x}
360:. Elements of parity 0 are said to be
3615:
2790:
2738:
1782:
1247:Further definitions and constructions
880:{\displaystyle xy\mapsto (-1)^{pq}yx}
309:, is a superalgebra over the ring of
2523:under the super tensor product with
974:Any algebra over a commutative ring
552:{\displaystyle yx=(-1)^{|x||y|}xy\,}
92:
2038:is, in general, different than the
1885:{\displaystyle =xy-(-1)^{|x||y|}yx}
1516:
581:
192:{\displaystyle A=A_{0}\oplus A_{1}}
13:
2818:Industrial and applied mathematics
2507:One may also define superalgebras
2070:may be regarded as a superalgebra
1949:
1251:
1166:
1163:
1160:
1135:
1132:
1129:
593:grading arises as a "rollup" of a
14:
4227:
3641:
3048:Stochastic differential equations
2642:Kac, Martinez & Zelmanov 2001
3667:Supersymmetric quantum mechanics
3364:Supersymmetric quantum mechanics
1797:is the binary operator given by
1199:forms a superalgebra denoted by
1092:
1089:
1086:
1069:
1066:
1063:
3246:Stochastic variational calculus
3038:Ordinary differential equations
1528:on any superalgebra called the
452:is one whose multiplication is
3043:Partial differential equations
2916:Arbitrary-precision arithmetic
2647:
2635:
2603:
2580:
2445:
2433:
2424:
2416:
2411:
2403:
2398:
2388:
2379:
2367:
2361:
2352:
2302:be a commutative superring. A
2251:
2205:
2199:
2184:
2179:
2164:
2159:
2149:
2143:
2117:
2114:
2088:
1992:
1980:
1959:
1953:
1930:is the set of all elements of
1870:
1862:
1857:
1849:
1844:
1834:
1819:
1807:
1751:
1741:
1732:
1618:
1580:
1572:
1567:
1557:
1548:
1474:
1462:
1441:
1429:
1390:
1173:{\displaystyle \mathrm {Hom} }
1142:{\displaystyle \mathrm {Hom} }
1108:
1096:
1079:
1073:
955:{\displaystyle q=n{\bmod {2}}}
919:{\displaystyle p=m{\bmod {2}}}
859:
849:
846:
635:
625:
622:
536:
528:
523:
515:
510:
500:
431:
423:
415:
407:
399:
388:
280:where the subscripts are read
1:
2931:Interactive geometry software
2678:
2461:for all homogeneous elements
1672:are the homogeneous parts of
1602:and on arbitrary elements by
578:in order to avoid confusion.
562:for all homogeneous elements
460:is one with a multiplicative
1301:The set of all odd elements
1240:universal enveloping algebra
438:{\displaystyle |xy|=|x|+|y|}
364:and those of parity 1 to be
319:The elements of each of the
7:
3662:Supersymmetric gauge theory
2983:Computational number theory
2946:Numerical-analysis software
968:
890:with the parities given as
10:
4232:
3961:Pure 4D N = 1 supergravity
2547:with two (even) morphisms
4092:
4009:
3951:
3895:
3869:
3861:Electricâmagnetic duality
3758:
3695:
3649:
3581:
3543:
3527:
3489:
3441:
3389:Algebra of physical space
3254:
3212:
3006:
2968:
2856:Automated theorem proving
2824:
2531:can then be defined as a
2324:-bilinear multiplication
336:of a homogeneous element
61:comes from the theory of
3882:HaagâĆopuszaĆskiâSohnius
3856:Little hierarchy problem
3182:Numerical linear algebra
2629:
1029:supercommutative algebra
780:{\displaystyle n=\deg y}
700:{\displaystyle m=\deg x}
606:one has an exchange map
470:commutative superalgebra
450:associative superalgebra
105:. In most applications,
3938:6D (2,0) superconformal
2921:Finite element analysis
2871:Constraint satisfaction
1899:by linearity. Elements
1290:. It forms an ordinary
1286:, naturally called the
1234:are a graded analog of
1040:alternating polynomials
3918:N = 4 super YangâMills
3908:N = 1 super YangâMills
3816:Supersymmetry breaking
3720:Superconformal algebra
3715:Super-Poincaré algebra
3476:Mathematical economics
3150:Multivariable calculus
3033:Differential equations
2876:Constraint programming
2866:Computational geometry
2617:
2519:-supermodules forms a
2452:
2261:
2025:
1886:
1773:
1654:
1593:
1481:
1407:
1278:and therefore forms a
1191:The set of all square
1174:
1143:
1115:
956:
920:
881:
824:
801:
781:
755:the parity. Likewise,
749:
729:
701:
666:
553:
439:
271:
193:
3996:Type IIB supergravity
3991:Type IIA supergravity
3966:4D N = 1 supergravity
3831:SeibergâWitten theory
3745:Super Minkowski space
3725:Supersymmetry algebra
3429:Supersymmetry algebra
3414:Representation theory
3409:Renormalization group
3055:Differential geometry
2936:Optimization software
2908:Mathematical software
2618:
2453:
2262:
2062:of two superalgebras
2026:
1887:
1774:
1655:
1594:
1521:There is a canonical
1482:
1408:
1175:
1144:
1121:, where the boldface
1116:
1036:symmetric polynomials
982:; that is, by taking
957:
921:
882:
825:
802:
782:
750:
730:
702:
667:
554:
440:
272:
194:
4216:Super linear algebra
3781:Short supermultiplet
3481:Mathematical finance
3466:Social choice theory
3381:Algebraic structures
3330:in quantum mechanics
3266:Analytical mechanics
3232:Stochastic processes
3204:Variational calculus
3016:Approximation theory
2941:Statistical software
2670:Deligne's discussion
2554:
2343:
2085:
2054:Super tensor product
1945:
1804:
1695:
1609:
1539:
1423:
1344:
1156:
1125:
1059:
930:
894:
837:
811:
791:
759:
739:
719:
679:
613:
488:
384:
225:
157:
71:super linear algebra
42:. That is, it is an
4001:Gauged supergravity
3986:Type I supergravity
3943:ABJM superconformal
3740:Harmonic superspace
3456:Operations research
3325:Perturbation theory
3123:Multilinear algebra
3094:Functional analysis
2951:Numerical libraries
2883:Computational logic
2672:of these two cases.
2535:in the category of
2034:The supercenter of
2003: for all
1019:In particular, any
458:unital superalgebra
340:, denoted by |
25:theoretical physics
3976:Higher dimensional
3971:N = 8 supergravity
3887:Nonrenormalization
3682:Super vector space
3677:Superstring theory
3593:Mathematics portal
3490:Other applications
3214:Probability theory
3197:Validated numerics
3177:Numerical analysis
3070:Geometric analysis
3060:Differential forms
2893:Information theory
2764:Varadarajan, V. S.
2613:
2611:
2448:
2257:
2021:
1882:
1783:Supercommutativity
1769:
1650:
1589:
1477:
1403:
1186:super vector space
1184:linear maps) of a
1170:
1149:is referred to as
1139:
1111:
952:
916:
877:
823:{\displaystyle q.}
820:
797:
777:
745:
725:
697:
662:
549:
481:is commutative if
435:
267:
189:
4198:
4197:
3841:WessâZumino gauge
3609:
3608:
3443:Decision sciences
3437:
3436:
3419:Spacetime algebra
3111:Harmonic analysis
3077:Dynamical systems
3021:Clifford analysis
2998:Discrete geometry
2964:
2963:
2779:978-0-8218-3574-6
2729:978-0-8218-2645-4
2521:monoidal category
2004:
1735:
1621:
1551:
1323:. The product in
1232:Lie superalgebras
1046:Clifford algebras
800:{\displaystyle y}
787:is the degree of
748:{\displaystyle p}
728:{\displaystyle x}
93:Formal definition
4223:
3981:11D supergravity
3710:Lie superalgebra
3697:Supermathematics
3636:
3629:
3622:
3613:
3612:
3394:Feynman integral
3377:
3376:
3337:Potential theory
3226:random variables
3116:Fourier analysis
3099:Operator algebra
3026:Clifford algebra
2978:Computer algebra
2904:
2903:
2811:
2804:
2797:
2788:
2787:
2783:
2757:
2733:
2712:; Martinez, C.;
2703:
2673:
2666:
2657:
2654:Varadarajan 2004
2651:
2645:
2639:
2622:
2620:
2619:
2614:
2612:
2457:
2455:
2454:
2449:
2429:
2428:
2427:
2419:
2414:
2406:
2266:
2264:
2263:
2258:
2250:
2249:
2240:
2239:
2227:
2226:
2217:
2216:
2204:
2203:
2202:
2197:
2196:
2187:
2182:
2177:
2176:
2167:
2142:
2141:
2129:
2128:
2113:
2112:
2100:
2099:
2030:
2028:
2027:
2022:
2005:
2002:
1952:
1918:
1891:
1889:
1888:
1883:
1875:
1874:
1873:
1865:
1860:
1852:
1778:
1776:
1775:
1770:
1759:
1758:
1737:
1736:
1728:
1707:
1706:
1659:
1657:
1656:
1651:
1649:
1648:
1636:
1635:
1623:
1622:
1614:
1598:
1596:
1595:
1590:
1585:
1584:
1583:
1575:
1553:
1552:
1544:
1530:grade involution
1517:Grade involution
1486:
1484:
1483:
1478:
1412:
1410:
1409:
1404:
1402:
1401:
1389:
1388:
1379:
1378:
1377:
1376:
1362:
1361:
1195:with entries in
1179:
1177:
1176:
1171:
1169:
1148:
1146:
1145:
1140:
1138:
1120:
1118:
1117:
1112:
1095:
1072:
1021:exterior algebra
1010:polynomial rings
961:
959:
958:
953:
951:
950:
925:
923:
922:
917:
915:
914:
886:
884:
883:
878:
870:
869:
829:
827:
826:
821:
807:and with parity
806:
804:
803:
798:
786:
784:
783:
778:
754:
752:
751:
746:
734:
732:
731:
726:
706:
704:
703:
698:
671:
669:
668:
663:
655:
654:
582:Sign conventions
576:supercommutative
558:
556:
555:
550:
541:
540:
539:
531:
526:
518:
477:. Specifically,
462:identity element
444:
442:
441:
436:
434:
426:
418:
410:
402:
391:
345:
276:
274:
273:
268:
266:
265:
247:
246:
237:
236:
202:together with a
198:
196:
195:
190:
188:
187:
175:
174:
103:commutative ring
79:graded manifolds
48:commutative ring
4231:
4230:
4226:
4225:
4224:
4222:
4221:
4220:
4201:
4200:
4199:
4194:
4088:
4005:
3947:
3891:
3877:ColemanâMandula
3865:
3826:Seiberg duality
3821:Konishi anomaly
3754:
3691:
3645:
3640:
3610:
3605:
3577:
3539:
3523:
3485:
3433:
3399:Poisson algebra
3375:
3257:
3250:
3208:
3104:Operator theory
3002:
2960:
2926:Tensor software
2902:
2851:Automata theory
2820:
2815:
2780:
2754:
2730:
2700:
2681:
2676:
2667:
2660:
2652:
2648:
2640:
2636:
2632:
2610:
2609:
2593:
2587:
2586:
2564:
2557:
2555:
2552:
2551:
2488:as a superring
2423:
2415:
2410:
2402:
2401:
2397:
2344:
2341:
2340:
2292:
2245:
2241:
2235:
2231:
2222:
2218:
2212:
2208:
2198:
2192:
2188:
2183:
2178:
2172:
2168:
2163:
2162:
2158:
2137:
2133:
2124:
2120:
2108:
2104:
2095:
2091:
2086:
2083:
2082:
2056:
2001:
1948:
1946:
1943:
1942:
1916:
1869:
1861:
1856:
1848:
1847:
1843:
1805:
1802:
1801:
1790:supercommutator
1785:
1754:
1750:
1727:
1726:
1702:
1698:
1696:
1693:
1692:
1671:
1644:
1640:
1631:
1627:
1613:
1612:
1610:
1607:
1606:
1579:
1571:
1570:
1566:
1543:
1542:
1540:
1537:
1536:
1519:
1508:
1424:
1421:
1420:
1397:
1393:
1384:
1380:
1372:
1368:
1367:
1363:
1357:
1353:
1345:
1342:
1341:
1333:
1314:
1307:
1288:even subalgebra
1273:
1254:
1252:Even subalgebra
1249:
1211:
1159:
1157:
1154:
1153:
1128:
1126:
1123:
1122:
1085:
1062:
1060:
1057:
1056:
1051:The set of all
1006:tensor algebras
988:
971:
946:
942:
931:
928:
927:
910:
906:
895:
892:
891:
862:
858:
838:
835:
834:
812:
809:
808:
792:
789:
788:
760:
757:
756:
740:
737:
736:
720:
717:
716:
707:is the degree (
680:
677:
676:
638:
634:
614:
611:
610:
592:
584:
535:
527:
522:
514:
513:
509:
489:
486:
485:
430:
422:
414:
406:
398:
387:
385:
382:
381:
359:
352:
341:
328:are said to be
327:
304:
290:
255:
251:
242:
238:
232:
228:
226:
223:
222:
206:multiplication
183:
179:
170:
166:
158:
155:
154:
95:
37:
17:
12:
11:
5:
4229:
4219:
4218:
4213:
4196:
4195:
4193:
4192:
4187:
4182:
4177:
4172:
4167:
4162:
4157:
4152:
4147:
4142:
4137:
4132:
4127:
4122:
4117:
4112:
4107:
4102:
4096:
4094:
4090:
4089:
4087:
4086:
4081:
4076:
4071:
4066:
4061:
4056:
4051:
4046:
4041:
4036:
4031:
4026:
4021:
4015:
4013:
4007:
4006:
4004:
4003:
3998:
3993:
3988:
3983:
3978:
3973:
3968:
3963:
3957:
3955:
3949:
3948:
3946:
3945:
3940:
3935:
3930:
3925:
3920:
3915:
3910:
3905:
3899:
3897:
3896:Field theories
3893:
3892:
3890:
3889:
3884:
3879:
3873:
3871:
3867:
3866:
3864:
3863:
3858:
3853:
3848:
3843:
3838:
3833:
3828:
3823:
3818:
3813:
3808:
3803:
3798:
3793:
3791:Superpotential
3788:
3783:
3778:
3776:Supermultiplet
3773:
3768:
3762:
3760:
3756:
3755:
3753:
3752:
3747:
3742:
3737:
3732:
3727:
3722:
3717:
3712:
3707:
3701:
3699:
3693:
3692:
3690:
3689:
3684:
3679:
3674:
3669:
3664:
3659:
3653:
3651:
3650:General topics
3647:
3646:
3639:
3638:
3631:
3624:
3616:
3607:
3606:
3604:
3603:
3590:
3582:
3579:
3578:
3576:
3575:
3570:
3565:
3560:
3559:
3558:
3547:
3545:
3541:
3540:
3538:
3537:
3531:
3529:
3525:
3524:
3522:
3521:
3514:
3509:
3504:
3499:
3493:
3491:
3487:
3486:
3484:
3483:
3478:
3473:
3468:
3463:
3458:
3453:
3447:
3445:
3439:
3438:
3435:
3434:
3432:
3431:
3426:
3421:
3416:
3411:
3406:
3401:
3396:
3391:
3385:
3383:
3374:
3373:
3372:
3371:
3366:
3356:
3355:
3354:
3349:
3339:
3334:
3333:
3332:
3322:
3321:
3320:
3315:
3310:
3305:
3300:
3295:
3290:
3280:
3279:
3278:
3273:
3262:
3260:
3252:
3251:
3249:
3248:
3243:
3238:
3229:
3218:
3216:
3210:
3209:
3207:
3206:
3201:
3200:
3199:
3194:
3189:
3184:
3174:
3173:
3172:
3167:
3162:
3157:
3147:
3146:
3145:
3140:
3135:
3130:
3120:
3119:
3118:
3108:
3107:
3106:
3101:
3091:
3090:
3089:
3087:Control theory
3084:
3074:
3073:
3072:
3067:
3062:
3052:
3051:
3050:
3045:
3040:
3030:
3029:
3028:
3018:
3012:
3010:
3004:
3003:
3001:
3000:
2995:
2990:
2985:
2980:
2974:
2972:
2966:
2965:
2962:
2961:
2959:
2958:
2953:
2948:
2943:
2938:
2933:
2928:
2923:
2918:
2912:
2910:
2901:
2900:
2895:
2890:
2885:
2880:
2879:
2878:
2868:
2863:
2858:
2853:
2848:
2847:
2846:
2841:
2830:
2828:
2822:
2821:
2814:
2813:
2806:
2799:
2791:
2785:
2784:
2778:
2759:
2758:
2752:
2735:
2734:
2728:
2705:
2704:
2698:
2680:
2677:
2675:
2674:
2658:
2646:
2633:
2631:
2628:
2624:
2623:
2608:
2605:
2602:
2599:
2596:
2594:
2592:
2589:
2588:
2585:
2582:
2579:
2576:
2573:
2570:
2567:
2565:
2563:
2560:
2559:
2459:
2458:
2447:
2444:
2441:
2438:
2435:
2432:
2426:
2422:
2418:
2413:
2409:
2405:
2400:
2396:
2393:
2390:
2387:
2384:
2381:
2378:
2375:
2372:
2369:
2366:
2363:
2360:
2357:
2354:
2351:
2348:
2291:
2288:
2268:
2267:
2256:
2253:
2248:
2244:
2238:
2234:
2230:
2225:
2221:
2215:
2211:
2207:
2201:
2195:
2191:
2186:
2181:
2175:
2171:
2166:
2161:
2157:
2154:
2151:
2148:
2145:
2140:
2136:
2132:
2127:
2123:
2119:
2116:
2111:
2107:
2103:
2098:
2094:
2090:
2060:tensor product
2055:
2052:
2032:
2031:
2020:
2017:
2014:
2011:
2008:
2000:
1997:
1994:
1991:
1988:
1985:
1982:
1979:
1976:
1973:
1970:
1967:
1964:
1961:
1958:
1955:
1951:
1893:
1892:
1881:
1878:
1872:
1868:
1864:
1859:
1855:
1851:
1846:
1842:
1839:
1836:
1833:
1830:
1827:
1824:
1821:
1818:
1815:
1812:
1809:
1784:
1781:
1780:
1779:
1768:
1765:
1762:
1757:
1753:
1749:
1746:
1743:
1740:
1734:
1731:
1725:
1722:
1719:
1716:
1713:
1710:
1705:
1701:
1667:
1661:
1660:
1647:
1643:
1639:
1634:
1630:
1626:
1620:
1617:
1600:
1599:
1588:
1582:
1578:
1574:
1569:
1565:
1562:
1559:
1556:
1550:
1547:
1518:
1515:
1506:
1488:
1487:
1476:
1473:
1470:
1467:
1464:
1461:
1458:
1455:
1452:
1449:
1446:
1443:
1440:
1437:
1434:
1431:
1428:
1414:
1413:
1400:
1396:
1392:
1387:
1383:
1375:
1371:
1366:
1360:
1356:
1352:
1349:
1331:
1312:
1305:
1271:
1253:
1250:
1248:
1245:
1244:
1243:
1229:
1203:
1189:
1180:, composed of
1168:
1165:
1162:
1137:
1134:
1131:
1110:
1107:
1104:
1101:
1098:
1094:
1091:
1088:
1084:
1081:
1078:
1075:
1071:
1068:
1065:
1049:
1043:
1032:
1017:
1002:graded algebra
990:
989:to be trivial.
986:
970:
967:
964:Pierre Deligne
949:
945:
941:
938:
935:
913:
909:
905:
902:
899:
888:
887:
876:
873:
868:
865:
861:
857:
854:
851:
848:
845:
842:
819:
816:
796:
776:
773:
770:
767:
764:
744:
724:
696:
693:
690:
687:
684:
673:
672:
661:
658:
653:
650:
647:
644:
641:
637:
633:
630:
627:
624:
621:
618:
603:graded algebra
590:
583:
580:
560:
559:
547:
544:
538:
534:
530:
525:
521:
517:
512:
508:
505:
502:
499:
496:
493:
433:
429:
425:
421:
417:
413:
409:
405:
401:
397:
394:
390:
357:
350:
323:
302:
288:
278:
277:
264:
261:
258:
254:
250:
245:
241:
235:
231:
200:
199:
186:
182:
178:
173:
169:
165:
162:
150:decomposition
115:characteristic
94:
91:
83:supermanifolds
40:graded algebra
35:
15:
9:
6:
4:
3:
2:
4228:
4217:
4214:
4212:
4209:
4208:
4206:
4191:
4188:
4186:
4183:
4181:
4178:
4176:
4173:
4171:
4168:
4166:
4163:
4161:
4158:
4156:
4153:
4151:
4148:
4146:
4143:
4141:
4138:
4136:
4133:
4131:
4128:
4126:
4123:
4121:
4118:
4116:
4113:
4111:
4108:
4106:
4103:
4101:
4098:
4097:
4095:
4091:
4085:
4082:
4080:
4077:
4075:
4072:
4070:
4067:
4065:
4062:
4060:
4057:
4055:
4052:
4050:
4047:
4045:
4042:
4040:
4037:
4035:
4032:
4030:
4027:
4025:
4022:
4020:
4017:
4016:
4014:
4012:
4011:Superpartners
4008:
4002:
3999:
3997:
3994:
3992:
3989:
3987:
3984:
3982:
3979:
3977:
3974:
3972:
3969:
3967:
3964:
3962:
3959:
3958:
3956:
3954:
3950:
3944:
3941:
3939:
3936:
3934:
3931:
3929:
3926:
3924:
3921:
3919:
3916:
3914:
3911:
3909:
3906:
3904:
3901:
3900:
3898:
3894:
3888:
3885:
3883:
3880:
3878:
3875:
3874:
3872:
3868:
3862:
3859:
3857:
3854:
3852:
3849:
3847:
3844:
3842:
3839:
3837:
3834:
3832:
3829:
3827:
3824:
3822:
3819:
3817:
3814:
3812:
3809:
3807:
3804:
3802:
3799:
3797:
3794:
3792:
3789:
3787:
3784:
3782:
3779:
3777:
3774:
3772:
3769:
3767:
3764:
3763:
3761:
3757:
3751:
3750:Supermanifold
3748:
3746:
3743:
3741:
3738:
3736:
3733:
3731:
3728:
3726:
3723:
3721:
3718:
3716:
3713:
3711:
3708:
3706:
3703:
3702:
3700:
3698:
3694:
3688:
3687:Supergeometry
3685:
3683:
3680:
3678:
3675:
3673:
3670:
3668:
3665:
3663:
3660:
3658:
3657:Supersymmetry
3655:
3654:
3652:
3648:
3644:
3643:Supersymmetry
3637:
3632:
3630:
3625:
3623:
3618:
3617:
3614:
3602:
3598:
3594:
3591:
3589:
3588:
3584:
3583:
3580:
3574:
3571:
3569:
3566:
3564:
3561:
3557:
3554:
3553:
3552:
3549:
3548:
3546:
3544:Organizations
3542:
3536:
3533:
3532:
3530:
3526:
3519:
3515:
3513:
3510:
3508:
3505:
3503:
3500:
3498:
3495:
3494:
3492:
3488:
3482:
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3459:
3457:
3454:
3452:
3449:
3448:
3446:
3444:
3440:
3430:
3427:
3425:
3422:
3420:
3417:
3415:
3412:
3410:
3407:
3405:
3404:Quantum group
3402:
3400:
3397:
3395:
3392:
3390:
3387:
3386:
3384:
3382:
3378:
3370:
3367:
3365:
3362:
3361:
3360:
3359:Supersymmetry
3357:
3353:
3350:
3348:
3345:
3344:
3343:
3342:String theory
3340:
3338:
3335:
3331:
3328:
3327:
3326:
3323:
3319:
3316:
3314:
3311:
3309:
3306:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3286:
3285:
3284:
3281:
3277:
3274:
3272:
3269:
3268:
3267:
3264:
3263:
3261:
3259:
3253:
3247:
3244:
3242:
3241:Path integral
3239:
3237:
3233:
3230:
3227:
3223:
3222:Distributions
3220:
3219:
3217:
3215:
3211:
3205:
3202:
3198:
3195:
3193:
3190:
3188:
3185:
3183:
3180:
3179:
3178:
3175:
3171:
3168:
3166:
3163:
3161:
3158:
3156:
3153:
3152:
3151:
3148:
3144:
3141:
3139:
3136:
3134:
3131:
3129:
3126:
3125:
3124:
3121:
3117:
3114:
3113:
3112:
3109:
3105:
3102:
3100:
3097:
3096:
3095:
3092:
3088:
3085:
3083:
3080:
3079:
3078:
3075:
3071:
3068:
3066:
3063:
3061:
3058:
3057:
3056:
3053:
3049:
3046:
3044:
3041:
3039:
3036:
3035:
3034:
3031:
3027:
3024:
3023:
3022:
3019:
3017:
3014:
3013:
3011:
3009:
3005:
2999:
2996:
2994:
2991:
2989:
2988:Combinatorics
2986:
2984:
2981:
2979:
2976:
2975:
2973:
2971:
2967:
2957:
2954:
2952:
2949:
2947:
2944:
2942:
2939:
2937:
2934:
2932:
2929:
2927:
2924:
2922:
2919:
2917:
2914:
2913:
2911:
2909:
2905:
2899:
2896:
2894:
2891:
2889:
2886:
2884:
2881:
2877:
2874:
2873:
2872:
2869:
2867:
2864:
2862:
2861:Coding theory
2859:
2857:
2854:
2852:
2849:
2845:
2842:
2840:
2837:
2836:
2835:
2832:
2831:
2829:
2827:
2826:Computational
2823:
2819:
2812:
2807:
2805:
2800:
2798:
2793:
2792:
2789:
2781:
2775:
2771:
2770:
2765:
2761:
2760:
2755:
2753:3-540-61378-1
2749:
2745:
2741:
2737:
2736:
2731:
2725:
2721:
2720:
2715:
2711:
2707:
2706:
2701:
2699:0-8218-2012-5
2695:
2691:
2687:
2683:
2682:
2671:
2665:
2663:
2655:
2650:
2643:
2638:
2634:
2627:
2606:
2600:
2597:
2595:
2590:
2583:
2577:
2574:
2571:
2568:
2566:
2561:
2550:
2549:
2548:
2546:
2543:-supermodule
2542:
2538:
2534:
2530:
2526:
2522:
2518:
2514:
2510:
2509:categorically
2505:
2503:
2499:
2495:
2491:
2487:
2482:
2480:
2476:
2472:
2468:
2464:
2442:
2439:
2436:
2430:
2420:
2407:
2394:
2391:
2385:
2382:
2376:
2373:
2370:
2364:
2358:
2355:
2349:
2346:
2339:
2338:
2337:
2335:
2331:
2327:
2323:
2319:
2316:
2314:
2309:
2305:
2301:
2296:
2287:
2285:
2281:
2277:
2273:
2254:
2246:
2242:
2236:
2232:
2228:
2223:
2219:
2213:
2209:
2193:
2189:
2173:
2169:
2155:
2152:
2146:
2138:
2134:
2130:
2125:
2121:
2109:
2105:
2101:
2096:
2092:
2081:
2080:
2079:
2077:
2073:
2069:
2065:
2061:
2051:
2049:
2045:
2041:
2037:
2018:
2012:
2009:
2006:
1998:
1995:
1989:
1986:
1983:
1977:
1974:
1971:
1968:
1962:
1956:
1941:
1940:
1939:
1937:
1933:
1929:
1925:
1920:
1914:
1910:
1906:
1902:
1898:
1879:
1876:
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1766:
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1666:
1645:
1641:
1637:
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1586:
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1563:
1560:
1554:
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1535:
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1527:
1524:
1514:
1512:
1505:
1501:
1497:
1493:
1471:
1468:
1465:
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1456:
1453:
1450:
1447:
1444:
1438:
1435:
1432:
1426:
1419:
1418:
1417:
1398:
1394:
1385:
1381:
1373:
1369:
1364:
1358:
1354:
1350:
1347:
1340:
1339:
1338:
1337:
1336:bilinear form
1330:
1326:
1322:
1318:
1311:
1304:
1299:
1297:
1293:
1289:
1285:
1281:
1277:
1270:
1267:
1263:
1259:
1241:
1237:
1233:
1230:
1227:
1223:
1219:
1215:
1210:
1206:
1202:
1198:
1194:
1193:supermatrices
1190:
1187:
1183:
1152:
1105:
1102:
1099:
1082:
1076:
1054:
1053:endomorphisms
1050:
1047:
1044:
1041:
1037:
1033:
1030:
1026:
1022:
1018:
1015:
1011:
1007:
1003:
999:
995:
991:
985:
981:
977:
973:
972:
966:
965:
947:
939:
936:
933:
911:
903:
900:
897:
874:
871:
866:
863:
855:
852:
843:
840:
833:
832:
831:
817:
814:
794:
774:
771:
768:
765:
762:
742:
722:
715:-grading) of
714:
710:
694:
691:
688:
685:
682:
659:
656:
651:
648:
645:
642:
639:
631:
628:
619:
616:
609:
608:
607:
604:
600:
596:
589:
579:
577:
573:
569:
565:
545:
542:
532:
519:
506:
503:
497:
494:
491:
484:
483:
482:
480:
476:
475:commutativity
472:
471:
465:
463:
459:
455:
451:
446:
427:
419:
411:
403:
395:
392:
379:
375:
371:
367:
363:
356:
349:
344:
339:
335:
331:
326:
322:
317:
315:
312:
308:
301:
297:
292:
287:
283:
262:
259:
256:
252:
248:
243:
239:
233:
229:
221:
220:
219:
217:
213:
209:
205:
184:
180:
176:
171:
167:
163:
160:
153:
152:
151:
149:
145:
142:
140:
135:
131:
126:
124:
120:
116:
112:
108:
104:
100:
90:
88:
84:
80:
76:
75:supergeometry
72:
68:
64:
63:supersymmetry
60:
55:
53:
49:
45:
41:
34:
30:
26:
22:
3953:Supergravity
3846:Localization
3836:Witten index
3811:Moduli space
3705:Superalgebra
3704:
3672:Supergravity
3599: /
3595: /
3585:
3461:Optimization
3424:Superalgebra
3423:
3283:Field theory
3256:Mathematical
3234: /
3082:Chaos theory
3065:Gauge theory
2993:Graph theory
2888:Cryptography
2768:
2743:
2740:Manin, Y. I.
2718:
2714:Zelmanov, E.
2689:
2656:, p. 87
2649:
2637:
2625:
2544:
2540:
2536:
2528:
2524:
2516:
2506:
2501:
2497:
2493:
2489:
2485:
2483:
2478:
2474:
2470:
2466:
2462:
2460:
2333:
2329:
2325:
2321:
2317:
2315:-supermodule
2312:
2307:
2304:superalgebra
2303:
2299:
2297:
2293:
2283:
2279:
2275:
2271:
2269:
2075:
2071:
2067:
2063:
2057:
2047:
2043:
2035:
2033:
1935:
1931:
1927:
1923:
1921:
1913:supercommute
1912:
1911:are said to
1908:
1904:
1900:
1896:
1894:
1794:
1788:
1786:
1685:
1677:
1673:
1668:
1664:
1662:
1601:
1529:
1526:automorphism
1520:
1510:
1503:
1499:
1495:
1491:
1489:
1415:
1328:
1324:
1320:
1309:
1302:
1300:
1295:
1287:
1283:
1275:
1268:
1261:
1257:
1255:
1236:Lie algebras
1225:
1221:
1217:
1213:
1208:
1204:
1200:
1196:
1181:
1150:
1024:
1013:
997:
993:
983:
979:
975:
889:
712:
708:
674:
598:
594:
587:
585:
575:
571:
567:
563:
561:
478:
468:
466:
457:
449:
447:
377:
373:
369:
365:
361:
354:
347:
342:
337:
333:
329:
324:
320:
318:
313:
299:
295:
293:
285:
279:
215:
211:
207:
201:
143:
138:
133:
130:superalgebra
129:
127:
122:
118:
106:
98:
96:
87:superschemes
67:supermodules
58:
56:
32:
29:superalgebra
28:
18:
4093:Researchers
4079:Stop squark
4044:Graviscalar
4039:Graviphoton
3903:WessâZumino
3766:Supercharge
3601:topics list
3535:Mathematics
3451:Game theory
3352:Topological
3318:Topological
3313:Statistical
3276:Hamiltonian
2686:Deligne, P.
2644:, p. 3
2058:The graded
1924:supercenter
454:associative
330:homogeneous
307:graded ring
117:0, such as
57:The prefix
21:mathematics
4205:Categories
4140:Iliopoulos
4084:Superghost
4074:Sgoldstino
4059:Neutralino
3851:Mu problem
3771:R-symmetry
3735:Superspace
3730:Supergroup
3507:Psychology
3471:Statistics
3271:Lagrangian
2898:Statistics
2834:Algorithms
2710:Kac, V. G.
2679:References
2270:If either
1523:involutive
1416:such that
1280:subalgebra
218:such that
148:direct sum
4110:Batchelor
4034:Goldstino
3923:Super QCD
3801:FI D-term
3786:BPS state
3512:Sociology
3502:Chemistry
3298:Effective
3293:Conformal
3288:Classical
3160:Geometric
3133:Geometric
2604:→
2591:η
2581:→
2575:⊗
2562:μ
2440:⋅
2392:−
2374:⋅
2350:⋅
2229:⊗
2153:−
2131:⊗
2102:⊗
2010:∈
1972:∈
1838:−
1832:−
1745:−
1733:^
1718:∈
1682:2-torsion
1638:−
1619:^
1561:−
1549:^
1469:⊗
1460:μ
1457:⋅
1445:⋅
1436:⊗
1427:μ
1391:→
1365:⊗
1348:μ
1266:submodule
1083:≡
1055:(denoted
853:−
847:↦
772:
692:
629:−
623:↦
586:When the
504:−
296:superring
249:⊆
177:⊕
4211:Algebras
4145:Montonen
4069:Sfermion
4064:R-hadron
4049:Higgsino
4024:Chargino
3913:4D N = 1
3870:Theorems
3759:Concepts
3587:Category
3236:analysis
3155:Exterior
3128:Exterior
3008:Analysis
2970:Discrete
2844:analysis
2766:(2004).
2742:(1997).
2716:(2001).
2513:category
2496:→
2477:∈
2465:∈
2332:→
2074:⊗
1490:for all
1317:bimodule
1220:of rank
1151:internal
969:Examples
311:integers
214:→
204:bilinear
4160:Seiberg
4135:Golfand
4115:Berezin
4100:Affleck
4029:Gaugino
3597:outline
3528:Related
3497:Biology
3347:Bosonic
3308:Quantum
3258:physics
3224: (
2956:Solvers
2515:of all
2328:×
2320:with a
1680:has no
1334:with a
1327:equips
1292:algebra
210:×
146:with a
141:-module
46:over a
44:algebra
4190:Zumino
4185:Witten
4175:Rogers
4165:Siegel
4105:Bagger
3806:F-term
3796:D-term
3170:Vector
3165:Tensor
3143:Vector
3138:Tensor
2839:design
2776:
2750:
2726:
2696:
2533:monoid
2511:. The
2040:center
1663:where
1498:, and
1308:is an
1264:. The
675:where
456:and a
334:parity
332:. The
282:modulo
59:super-
4170:RoÄek
4155:Salam
4150:Olive
4130:Gates
4125:Fayet
4019:Axino
3933:NMSSM
3303:Gauge
2630:Notes
2310:is a
2306:over
1676:. If
1294:over
1023:over
1012:over
996:- or
711:- or
597:- or
368:. If
298:, or
136:is a
132:over
111:field
109:is a
101:be a
52:field
31:is a
4180:Wess
4120:Dine
3928:MSSM
2774:ISBN
2748:ISBN
2724:ISBN
2694:ISBN
2668:See
2469:and
2298:Let
2282:and
2066:and
1922:The
1903:and
1787:The
1256:Let
1038:and
1034:The
1008:and
992:Any
926:and
735:and
566:and
380:and
372:and
362:even
97:Let
85:and
27:, a
23:and
4054:LSP
2274:or
2042:of
1926:of
1917:= 0
1915:if
1907:of
1793:on
1502:in
1282:of
1182:all
944:mod
908:mod
769:deg
689:deg
570:of
448:An
366:odd
353:or
121:or
113:of
50:or
19:In
4207::
2661:^
2504:.
2481:.
2473:,
2050:.
1938::
1919:.
1688::
1513:.
1494:,
1298:.
467:A
445:.
378:xy
316:.
294:A
291:.
128:A
125:.
89:.
81:,
3635:e
3628:t
3621:v
3520:"
3516:"
3228:)
2810:e
2803:t
2796:v
2782:.
2756:.
2732:.
2702:.
2607:A
2601:R
2598::
2584:A
2578:A
2572:A
2569::
2545:A
2541:R
2537:R
2529:R
2525:R
2517:R
2502:A
2498:A
2494:R
2490:A
2486:R
2479:A
2475:y
2471:x
2467:R
2463:r
2446:)
2443:y
2437:r
2434:(
2431:x
2425:|
2421:x
2417:|
2412:|
2408:r
2404:|
2399:)
2395:1
2389:(
2386:=
2383:y
2380:)
2377:x
2371:r
2368:(
2365:=
2362:)
2359:y
2356:x
2353:(
2347:r
2334:A
2330:A
2326:A
2322:R
2318:A
2313:R
2308:R
2300:R
2284:B
2280:A
2276:B
2272:A
2255:.
2252:)
2247:2
2243:b
2237:1
2233:b
2224:2
2220:a
2214:1
2210:a
2206:(
2200:|
2194:2
2190:a
2185:|
2180:|
2174:1
2170:b
2165:|
2160:)
2156:1
2150:(
2147:=
2144:)
2139:2
2135:b
2126:2
2122:a
2118:(
2115:)
2110:1
2106:b
2097:1
2093:a
2089:(
2076:B
2072:A
2068:B
2064:A
2048:A
2044:A
2036:A
2019:.
2016:}
2013:A
2007:x
1999:0
1996:=
1993:]
1990:x
1987:,
1984:a
1981:[
1978::
1975:A
1969:a
1966:{
1963:=
1960:)
1957:A
1954:(
1950:Z
1936:A
1932:A
1928:A
1909:A
1905:y
1901:x
1897:A
1880:x
1877:y
1871:|
1867:y
1863:|
1858:|
1854:x
1850:|
1845:)
1841:1
1835:(
1829:y
1826:x
1823:=
1820:]
1817:y
1814:,
1811:x
1808:[
1795:A
1767:.
1764:}
1761:x
1756:i
1752:)
1748:1
1742:(
1739:=
1730:x
1724::
1721:A
1715:x
1712:{
1709:=
1704:i
1700:A
1686:A
1678:A
1674:x
1669:i
1665:x
1646:1
1642:x
1633:0
1629:x
1625:=
1616:x
1587:x
1581:|
1577:x
1573:|
1568:)
1564:1
1558:(
1555:=
1546:x
1511:A
1507:1
1504:A
1500:z
1496:y
1492:x
1475:)
1472:z
1466:y
1463:(
1454:x
1451:=
1448:z
1442:)
1439:y
1433:x
1430:(
1399:0
1395:A
1386:1
1382:A
1374:0
1370:A
1359:1
1355:A
1351::
1332:1
1329:A
1325:A
1321:A
1315:-
1313:0
1310:A
1306:1
1303:A
1296:K
1284:A
1276:A
1272:0
1269:A
1262:K
1258:A
1226:q
1224:|
1222:p
1218:K
1214:K
1212:(
1209:q
1207:|
1205:p
1201:M
1197:K
1167:m
1164:o
1161:H
1136:m
1133:o
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1109:)
1106:V
1103:,
1100:V
1097:(
1093:m
1090:o
1087:H
1080:)
1077:V
1074:(
1070:d
1067:n
1064:E
1031:.
1025:K
1016:.
1014:K
1000:-
998:N
994:Z
987:1
984:A
980:K
976:K
948:2
940:n
937:=
934:q
912:2
904:m
901:=
898:p
875:x
872:y
867:q
864:p
860:)
856:1
850:(
844:y
841:x
818:.
815:q
795:y
775:y
766:=
763:n
743:p
723:x
713:N
709:Z
695:x
686:=
683:m
660:x
657:y
652:q
649:p
646:+
643:n
640:m
636:)
632:1
626:(
620:y
617:x
601:-
599:N
595:Z
591:2
588:Z
572:A
568:y
564:x
546:y
543:x
537:|
533:y
529:|
524:|
520:x
516:|
511:)
507:1
501:(
498:=
495:x
492:y
479:A
432:|
428:y
424:|
420:+
416:|
412:x
408:|
404:=
400:|
396:y
393:x
389:|
374:y
370:x
358:1
355:A
351:0
348:A
343:x
338:x
325:i
321:A
314:Z
305:-
303:2
300:Z
289:2
286:Z
263:j
260:+
257:i
253:A
244:j
240:A
234:i
230:A
216:A
212:A
208:A
185:1
181:A
172:0
168:A
164:=
161:A
144:A
139:K
134:K
123:C
119:R
107:K
99:K
38:-
36:2
33:Z
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