29:
It turns out that there are applications of our functors which make use of the analogous transformations which we like to think of as a change of basis for a fixed root-system — a tilting of the axes relative to the roots which results in a different subset of roots lying in the positive cone. ...
831:
1578:
1265:
1229:
1363:
1178:
1138:
982:
723:
679:
586:
632:
539:
886:
356:
because the module categories over such algebras are fairly well understood. The endomorphism algebra of a tilting module over a hereditary finite-dimensional algebra is called a
1415:
1391:
1098:
1074:
1042:
1018:
942:
914:
779:
755:
1829:
2195:
2153:
2086:
1869:
111:
1713:, so this is not a direct generalization of the finite-dimensional situation considered above. Given such a tilting object with endomorphism ring
726:
2181:
784:
2145:
1997:
1811:
1519:
1234:
1198:
1976:
Brenner, Sheila; Butler, Michael C. R. (1980), "Generalizations of the
Bernstein-Gel'fand-Ponomarev reflection functors",
1643:. Tilting complexes are generalizations of generalized tilting modules. A version of this theorem is valid for arbitrary
99:
2258:
1328:
1143:
1103:
947:
688:
1683:
of global dimension ≤ 2 such that every indecomposable module either has projective dimension ≤ 1 or
17:
2351:
2334:
637:
544:
595:
502:
847:
2329:
1795:
1665:
484:
154:
2324:
1944:
1396:
1372:
1079:
1055:
1023:
999:
923:
895:
760:
736:
1835:. In Balcerzyk, Stanisław; Józefiak, Tadeusz; Krempa, Jan; Simson, Daniel; Vogel, Wolfgang (eds.).
2028:
1782:
2245:, London Mathematical Society Lecture Notes Series, vol. 119, Cambridge University Press,
2116:
Cline, Edward; Parshall, Brian; Scott, Leonard (1986), "Derived categories and Morita theory",
1939:
326:
1448:
1192:
56:
1978:
Representation theory, II (Proc. Second
Internat. Conf., Carleton Univ., Ottawa, Ont., 1979)
126:) who introduced tilting functors. Dieter Happel and Claus Michael Ringel (
2276:
2234:
2137:
2109:
2061:
2007:
1969:
1931:
1908:
1852:
1821:
842:
180:
162:
103:
2267:
Happel, Dieter (2001), "A characterization of hereditary categories with tilting object",
8:
1684:
150:
146:
2280:
1935:
1691:
classified the hereditary abelian categories that can appear in the above construction.
2292:
2222:
2077:
2065:
2037:
2015:
1896:
1760:
1661:
1644:
1624:
1291:
1184:
1717:, they establish tilting functors that provide equivalences between a torsion pair in
2296:
2254:
2214:
2179:; Smalø, Sverre O. (1996), "Tilting in abelian categories and quasitilted algebras",
2129:
1993:
1957:
1888:
1860:
1807:
247:
188:
107:
76:
2069:
1953:
1786:
30:
For this reason, and because the word 'tilt' inflects easily, we call our functors
2312:
2284:
2246:
2243:
Triangulated categories in the representation theory of finite-dimensional algebras
2204:
2162:
2125:
2095:
2047:
1985:
1949:
1915:
1878:
1840:
1799:
1436:
1275:
462:
231:
87:
2167:
2100:
130:) defined tilted algebras and tilting modules as further generalizations of this.
2230:
2133:
2105:
2057:
2023:
2003:
1981:
1965:
1904:
1848:
1817:
1736:
349:
184:
64:
122:), and generalized by Sheila Brenner and Michael C. R. Butler (
2316:
1919:
1514:
143:
91:
2052:
1709:
contain the direct sums of arbitrary (possibly infinite) numbers of copies of
2345:
2250:
2218:
1961:
1892:
1803:
1767:
summarizes all the module categories of cluster tilted algebras arising from
1839:. Banach Center Publications. Vol. 26. Warsaw: PWN. pp. 127–180.
2288:
1844:
1595:
These generalized tilting modules also yield derived equivalences between
2176:
2081:
2019:
1864:
1485:
488:
310:
198:
115:
52:
2226:
1989:
1900:
235:
1922:; Ponomarev, V. A. (1973), "Coxeter functors, and Gabriel's theorem",
1675:, a generalization of tilted algebras. The quasi-tilted algebras over
1100:. (Note that these equivalences switch the order of the torsion pairs
2042:
1759:. A cluster tilted algebra arises from a tilted algebra as a certain
826:{\displaystyle \operatorname {Hom} ({\mathcal {T}},{\mathcal {F}})=0}
192:
2209:
1883:
1794:, London Mathematical Society Lecture Note Series, vol. 332,
1664:
in which all Hom- and Ext-spaces are finite-dimensional over some
2193:
Happel, Dieter; Ringel, Claus
Michael (1982), "Tilted algebras",
83:
2303:
Rickard, Jeremy (1989), "Morita theory for derived categories",
82:
Tilting theory was motivated by the introduction of reflection
2146:"Tilting Objects in Abelian Categories and Quasitilted Rings"
1671:. The endomorphism algebras of these tilting objects are the
1980:, Lecture Notes in Math., vol. 832, Berlin, New York:
1781:
263: ). This is another finite-dimensional algebra, and
238:
morphism between finite direct sums of direct summands of
1914:
95:
1639:
is the endomorphism algebra of a "tilting complex" over
1282:
also has finite global dimension, and the difference of
1859:
1573:{\displaystyle 0\to A\to T_{1}\to \dots \to T_{n}\to 0}
119:
2013:
1744:
1522:
1399:
1375:
1331:
1260:{\displaystyle {\mathcal {Y}}=\operatorname {mod} -B}
1237:
1224:{\displaystyle {\mathcal {T}}=\operatorname {mod} -A}
1201:
1146:
1106:
1082:
1058:
1026:
1002:
950:
926:
898:
850:
787:
763:
739:
691:
640:
598:
547:
505:
2026:(2006), "Tilting theory and cluster combinatorics",
1679:are precisely the finite-dimensional algebras over
499:. Specifically, if we define the two subcategories
2144:Colpi, Riccardo; Fuller, Kent R. (February 2007),
2115:
1572:
1424:
1409:
1385:
1357:
1259:
1223:
1183:Tilting theory may be seen as a generalization of
1172:
1132:
1092:
1068:
1036:
1012:
976:
936:
908:
880:
825:
773:
749:
717:
673:
626:
580:
533:
2196:Transactions of the American Mathematical Society
2174:
2154:Transactions of the American Mathematical Society
2087:Transactions of the American Mathematical Society
1870:Transactions of the American Mathematical Society
1657:
1454:
2343:
1785:; Happel, Dieter; Krause, Henning, eds. (2007),
988:-mod. Further, the restrictions of the functors
2075:
1752:
1623:extended the results on derived equivalence by
1358:{\displaystyle ({\mathcal {X}},{\mathcal {Y}})}
1173:{\displaystyle ({\mathcal {X}},{\mathcal {Y}})}
1133:{\displaystyle ({\mathcal {T}},{\mathcal {F}})}
977:{\displaystyle ({\mathcal {X}},{\mathcal {Y}})}
718:{\displaystyle ({\mathcal {T}},{\mathcal {F}})}
1321:is a tilted algebra), the global dimension of
1975:
1867:(1979), "Coxeter functors without diagrams",
1587:are finite direct sums of direct summands of
480:
123:
43:
2192:
2182:Memoirs of the American Mathematical Society
1365:splits, i.e. every indecomposable object of
781:are maximal subcategories with the property
127:
79:of a tilting module over the first algebra.
2143:
1694:
246:Given such a tilting module, we define the
2305:Journal of the London Mathematical Society
172:if it has the following three properties:
2208:
2166:
2099:
2051:
2041:
1943:
1882:
1837:Topics in algebra, Part 1 (Warsaw, 1988)
2302:
1620:
674:{\displaystyle {\mathcal {Y}}=\ker(G')}
581:{\displaystyle {\mathcal {T}}=\ker(F')}
14:
2344:
2266:
2240:
1688:
1660:defined tilting objects in hereditary
1635:are derived equivalent if and only if
1420:
627:{\displaystyle {\mathcal {X}}=\ker(G)}
534:{\displaystyle {\mathcal {F}}=\ker(F)}
106:. These functors were reformulated by
98:); these functors were used to relate
2322:
1827:
1755:) associated to a hereditary algebra
1627:that two finite-dimensional algebras
1475:with the following three properties:
881:{\displaystyle 0\to U\to M\to V\to 0}
1463:over the finite-dimensional algebra
94:, and V. A. Ponomarev (
2084:(2007), "Cluster-tilted algebras",
1325:is at most 2, and the torsion pair
1052:yield inverse equivalences between
996:yield inverse equivalences between
24:
1425:Cline, Parshall & Scott (1986)
1402:
1378:
1347:
1337:
1240:
1204:
1162:
1152:
1122:
1112:
1085:
1061:
1029:
1005:
966:
956:
929:
901:
809:
799:
766:
742:
707:
697:
643:
601:
550:
508:
483:showed that tilting functors give
183:at most 1, in other words it is a
75:. Here, the second algebra is the
25:
2363:
1705:; their definition requires that
1701:in an arbitrary abelian category
1658:Happel, Reiten & Smalø (1996)
1435:are derived equivalent (i.e. the
372:is a finite-dimensional algebra,
1830:"Tilting theory–an introduction"
1482:has finite projective dimension.
1290:induces an isometry between the
592:-mod, and the two subcategories
348:In practice one often considers
67:of two algebras using so-called
1954:10.1070/RM1973v028n02ABEH001526
1753:Buan, Marsh & Reiten (2007)
1763:, and the cluster category of
1564:
1551:
1545:
1532:
1526:
1455:Generalizations and extensions
1410:{\displaystyle {\mathcal {Y}}}
1386:{\displaystyle {\mathcal {X}}}
1352:
1332:
1167:
1147:
1127:
1107:
1093:{\displaystyle {\mathcal {X}}}
1069:{\displaystyle {\mathcal {F}}}
1037:{\displaystyle {\mathcal {Y}}}
1013:{\displaystyle {\mathcal {T}}}
971:
951:
937:{\displaystyle {\mathcal {F}}}
909:{\displaystyle {\mathcal {T}}}
872:
866:
860:
854:
814:
794:
774:{\displaystyle {\mathcal {F}}}
750:{\displaystyle {\mathcal {T}}}
712:
692:
668:
657:
621:
615:
575:
564:
528:
522:
133:
63:describes a way to relate the
13:
1:
2168:10.1090/s0002-9947-06-03909-2
2101:10.1090/s0002-9947-06-03879-7
1774:
337:-modules to the category mod-
267:is a finitely-generated left
2130:10.1016/0021-8693(86)90224-3
1924:Russian Mathematical Surveys
1044:, while the restrictions of
352:finite-dimensional algebras
341:of finitely-generated right
333:of finitely-generated right
7:
2330:Encyclopedia of Mathematics
481:Brenner & Butler (1980)
10:
2368:
1796:Cambridge University Press
1788:Handbook of tilting theory
1666:algebraically closed field
1461:generalized tilting module
833:; this implies that every
44:Brenner & Butler (1980
2053:10.1016/j.aim.2005.06.003
1695:Colpi & Fuller (2007)
376:is a tilting module over
2317:10.1112/jlms/s2-39.3.436
2251:10.1017/CBO9780511629228
1863:; Platzeck, MarĂa InĂ©s;
1804:10.1017/CBO9780511735134
1697:defined tilting objects
1447:-mod) are equivalent as
363:
142:is a finite-dimensional
2241:Happel, Dieter (1988),
2029:Advances in Mathematics
1828:Assem, Ibrahim (1990).
1739:came the definition of
1449:triangulated categories
1427:showed that in general
1749:cluster tilted algebra
1725:-Mod, the category of
1721:and a torsion pair in
1574:
1411:
1387:
1359:
1261:
1225:
1187:which is recovered if
1174:
1134:
1094:
1070:
1038:
1014:
978:
938:
910:
882:
841:-mod admits a natural
827:
775:
751:
719:
675:
628:
582:
535:
40:
2352:Representation theory
2289:10.1007/s002220100135
1845:10.4064/-26-1-127-180
1783:Angeleri HĂĽgel, Lidia
1673:quasi-tilted algebras
1575:
1412:
1388:
1360:
1262:
1226:
1175:
1135:
1095:
1071:
1039:
1015:
984:is a torsion pair in
979:
939:
911:
883:
828:
776:
752:
720:
676:
629:
583:
536:
108:Maurice Auslander
57:representation theory
27:
1984:, pp. 103–169,
1520:
1397:
1373:
1329:
1317:is hereditary (i.e.
1235:
1199:
1193:projective generator
1144:
1104:
1080:
1056:
1024:
1000:
948:
924:
896:
848:
843:short exact sequence
785:
761:
737:
689:
638:
596:
545:
503:
473:is right adjoint to
248:endomorphism algebra
181:projective dimension
88:Joseph BernšteÄn
77:endomorphism algebra
2323:Unger, L. (2001) ,
2281:2001InMat.144..381H
2018:; Reineke, Markus;
1936:1973RuMaS..28...17B
1916:BernšteÄn, Iosif N.
1735:From the theory of
1685:injective dimension
1292:Grothendieck groups
300:,−), −⊗
147:associative algebra
112:MarĂa InĂ©s Platzeck
1990:10.1007/BFb0088461
1920:Gelfand, Izrail M.
1861:Auslander, Maurice
1761:semidirect product
1745:Buan et al. (2006)
1662:abelian categories
1570:
1437:derived categories
1407:
1383:
1369:-mod is either in
1355:
1257:
1221:
1185:Morita equivalence
1170:
1130:
1090:
1066:
1034:
1010:
974:
934:
906:
878:
823:
771:
747:
715:
671:
624:
578:
531:
155:finitely-generated
1999:978-3-540-10264-9
1813:978-0-521-68045-5
189:projective module
65:module categories
16:(Redirected from
2359:
2337:
2325:"Tilting theory"
2319:
2299:
2263:
2237:
2212:
2189:
2175:Happel, Dieter;
2171:
2170:
2150:
2140:
2112:
2103:
2072:
2055:
2045:
2024:Todorov, Gordana
2010:
1972:
1947:
1911:
1886:
1856:
1834:
1824:
1793:
1741:cluster category
1737:cluster algebras
1579:
1577:
1576:
1571:
1563:
1562:
1544:
1543:
1497:
1496:
1416:
1414:
1413:
1408:
1406:
1405:
1392:
1390:
1389:
1384:
1382:
1381:
1364:
1362:
1361:
1356:
1351:
1350:
1341:
1340:
1276:global dimension
1266:
1264:
1263:
1258:
1244:
1243:
1230:
1228:
1227:
1222:
1208:
1207:
1179:
1177:
1176:
1171:
1166:
1165:
1156:
1155:
1139:
1137:
1136:
1131:
1126:
1125:
1116:
1115:
1099:
1097:
1096:
1091:
1089:
1088:
1075:
1073:
1072:
1067:
1065:
1064:
1043:
1041:
1040:
1035:
1033:
1032:
1019:
1017:
1016:
1011:
1009:
1008:
983:
981:
980:
975:
970:
969:
960:
959:
943:
941:
940:
935:
933:
932:
915:
913:
912:
907:
905:
904:
887:
885:
884:
879:
832:
830:
829:
824:
813:
812:
803:
802:
780:
778:
777:
772:
770:
769:
756:
754:
753:
748:
746:
745:
724:
722:
721:
716:
711:
710:
701:
700:
680:
678:
677:
672:
667:
647:
646:
633:
631:
630:
625:
605:
604:
587:
585:
584:
579:
574:
554:
553:
540:
538:
537:
532:
512:
511:
487:between certain
452:
451:
422:
421:
394: ). Write
384: = End
320:
319:
295:
294:
273:tilting functors
253: = End
210:
209:
191:by a projective
73:tilting functors
47:
37:
33:
32:tilting functors
21:
2367:
2366:
2362:
2361:
2360:
2358:
2357:
2356:
2342:
2341:
2340:
2261:
2210:10.2307/1999116
2148:
2000:
1982:Springer-Verlag
1945:10.1.1.642.2527
1884:10.2307/1998978
1832:
1814:
1791:
1777:
1612:
1585:
1558:
1554:
1539:
1535:
1521:
1518:
1517:
1495:
1490:
1489:
1488:
1457:
1401:
1400:
1398:
1395:
1394:
1377:
1376:
1374:
1371:
1370:
1346:
1345:
1336:
1335:
1330:
1327:
1326:
1305:
1297:
1239:
1238:
1236:
1233:
1232:
1203:
1202:
1200:
1197:
1196:
1195:; in that case
1161:
1160:
1151:
1150:
1145:
1142:
1141:
1121:
1120:
1111:
1110:
1105:
1102:
1101:
1084:
1083:
1081:
1078:
1077:
1060:
1059:
1057:
1054:
1053:
1028:
1027:
1025:
1022:
1021:
1004:
1003:
1001:
998:
997:
965:
964:
955:
954:
949:
946:
945:
928:
927:
925:
922:
921:
900:
899:
897:
894:
893:
849:
846:
845:
808:
807:
798:
797:
786:
783:
782:
765:
764:
762:
759:
758:
741:
740:
738:
735:
734:
706:
705:
696:
695:
690:
687:
686:
660:
642:
641:
639:
636:
635:
600:
599:
597:
594:
593:
567:
549:
548:
546:
543:
542:
507:
506:
504:
501:
500:
450:
447:
446:
445:
436:
420:
415:
414:
413:
403:
389:
366:
318:
315:
314:
313:
305:
293:
288:
287:
286:
280:
258:
208:
203:
202:
201:
136:
100:representations
71:and associated
69:tilting modules
55:, specifically
49:
42:
35:
31:
23:
22:
18:Coxeter functor
15:
12:
11:
5:
2365:
2355:
2354:
2339:
2338:
2320:
2311:(2): 436–456,
2300:
2275:(2): 381–398,
2264:
2259:
2238:
2203:(2): 399–443,
2190:
2172:
2161:(2): 741–765,
2141:
2124:(2): 397–409,
2113:
2094:(1): 323–332,
2073:
2036:(2): 572–618,
2011:
1998:
1973:
1912:
1857:
1825:
1812:
1778:
1776:
1773:
1621:Rickard (1989)
1608:
1593:
1592:
1583:
1569:
1566:
1561:
1557:
1553:
1550:
1547:
1542:
1538:
1534:
1531:
1528:
1525:
1515:exact sequence
1511:
1506:) = 0 for all
1491:
1483:
1456:
1453:
1404:
1380:
1354:
1349:
1344:
1339:
1334:
1303:
1295:
1256:
1253:
1250:
1247:
1242:
1220:
1217:
1214:
1211:
1206:
1169:
1164:
1159:
1154:
1149:
1129:
1124:
1119:
1114:
1109:
1087:
1063:
1031:
1007:
973:
968:
963:
958:
953:
931:
903:
877:
874:
871:
868:
865:
862:
859:
856:
853:
822:
819:
816:
811:
806:
801:
796:
793:
790:
768:
744:
714:
709:
704:
699:
694:
670:
666:
663:
659:
656:
653:
650:
645:
623:
620:
617:
614:
611:
608:
603:
577:
573:
570:
566:
563:
560:
557:
552:
530:
527:
524:
521:
518:
515:
510:
448:
432:
416:
399:
385:
365:
362:
358:tilted algebra
316:
301:
289:
285:,−), Ext
276:
271:-module. The
254:
244:
243:
220:
204:
196:
170:tilting module
135:
132:
114:, and
92:Israel Gelfand
61:tilting theory
46:, p. 103)
26:
9:
6:
4:
3:
2:
2364:
2353:
2350:
2349:
2347:
2336:
2332:
2331:
2326:
2321:
2318:
2314:
2310:
2306:
2301:
2298:
2294:
2290:
2286:
2282:
2278:
2274:
2270:
2269:Invent. Math.
2265:
2262:
2260:9780521339223
2256:
2252:
2248:
2244:
2239:
2236:
2232:
2228:
2224:
2220:
2216:
2211:
2206:
2202:
2198:
2197:
2191:
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2184:
2183:
2178:
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2169:
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2160:
2156:
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2131:
2127:
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2119:
2114:
2111:
2107:
2102:
2097:
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2089:
2088:
2083:
2079:
2078:Marsh, Robert
2076:Buan, Aslak;
2074:
2071:
2067:
2063:
2059:
2054:
2049:
2044:
2039:
2035:
2031:
2030:
2025:
2021:
2017:
2016:Marsh, Robert
2014:Buan, Aslak;
2012:
2009:
2005:
2001:
1995:
1991:
1987:
1983:
1979:
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1967:
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1951:
1946:
1941:
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1696:
1692:
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1689:Happel (2001)
1686:
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1678:
1674:
1670:
1667:
1663:
1659:
1655:
1653:
1649:
1646:
1642:
1638:
1634:
1630:
1626:
1622:
1618:
1616:
1611:
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1567:
1559:
1555:
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1523:
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1494:
1487:
1484:
1481:
1478:
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1466:
1462:
1452:
1450:
1446:
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1426:
1422:
1421:Happel (1988)
1418:
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1342:
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1309:
1301:
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1190:
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1047:
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863:
857:
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788:
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609:
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519:
516:
513:
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494:
490:
489:subcategories
486:
482:
478:
476:
472:
468:
464:
463:right adjoint
460:
456:
443:
439:
435:
430:
426:
419:
411:
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402:
397:
393:
388:
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332:
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324:
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218:
214:
207:
200:
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186:
182:
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175:
174:
173:
171:
167:
164:
160:
156:
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148:
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141:
138:Suppose that
131:
129:
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101:
97:
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2180:
2177:Reiten, Idun
2158:
2152:
2121:
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2091:
2085:
2082:Reiten, Idun
2043:math/0402054
2033:
2027:
2020:Reiten, Idun
1977:
1930:(2): 17–32,
1927:
1923:
1874:
1868:
1865:Reiten, Idun
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1768:
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1729:
1726:
1722:
1718:
1714:
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1507:
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727:torsion pair
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485:equivalences
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169:
168:is called a
165:
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1687:≤ 1.
1467:is a right
1274:has finite
733:-mod (i.e.
685:-mod, then
427:,−),
408:,−),
134:Definitions
116:Idun Reiten
53:mathematics
34:or simply
1775:References
1732:-modules.
1617: ).
1580:where the
431:= −⊗
350:hereditary
345:-modules.
236:surjective
222:The right
149:over some
2335:EMS Press
2297:120437744
2219:0002-9947
1962:0042-1316
1940:CiteSeerX
1893:0002-9947
1565:→
1552:→
1549:⋯
1546:→
1533:→
1527:→
1252:−
1216:−
873:→
867:→
861:→
855:→
792:
655:
613:
562:
520:
453:(−,
321:(−,
193:submodule
2346:Category
2070:15318919
1877:: 1–46,
1603:, where
1471:-module
1313:In case
1050:G′
1046:F′
665:′
572:′
495:and mod-
475:G′
471:F′
442:G′
410:F′
368:Suppose
327:category
226:-module
185:quotient
84:functors
2277:Bibcode
2235:0675063
2227:1999116
2138:0866784
2118:Algebra
2110:2247893
2062:2249625
2008:0607151
1970:0393065
1932:Bibcode
1909:0530043
1901:1998978
1853:1171230
1822:2385175
1625:proving
1510:> 0.
1302:) and K
1278:, then
491:of mod-
230:is the
118: (
104:quivers
102:of two
2295:
2257:
2233:
2225:
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2060:
2006:
1996:
1968:
1960:
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1743:(from
1393:or in
944:) and
440:, and
380:, and
232:kernel
163:module
157:right
144:unital
110:,
90:,
2293:S2CID
2223:JSTOR
2149:(PDF)
2066:S2CID
2038:arXiv
1897:JSTOR
1833:(PDF)
1792:(PDF)
1645:rings
1607:= End
1191:is a
888:with
725:is a
444:= Tor
412:= Ext
398:= Hom
364:Facts
234:of a
187:of a
151:field
36:tilts
2255:ISBN
2215:ISSN
1994:ISBN
1958:ISSN
1889:ISSN
1808:ISBN
1650:and
1631:and
1599:and
1431:and
1423:and
1286:and
1231:and
1140:and
1076:and
1048:and
1020:and
992:and
916:and
757:and
634:and
541:and
469:and
329:mod-
309:and
179:has
153:. A
128:1982
124:1980
120:1979
96:1973
2313:doi
2285:doi
2273:144
2247:doi
2205:doi
2201:274
2187:575
2163:doi
2159:359
2126:doi
2122:104
2096:doi
2092:359
2048:doi
2034:204
1986:doi
1950:doi
1879:doi
1875:250
1841:doi
1800:doi
1727:all
1486:Ext
1451:).
1310:).
1270:If
1249:mod
1213:mod
1180:.)
920:in
892:in
837:in
789:Hom
729:in
681:of
652:ker
610:ker
588:of
559:ker
517:ker
465:to
461:is
457:).
311:Tor
275:Hom
199:Ext
86:by
51:In
2348::
2333:,
2327:,
2309:39
2307:,
2291:,
2283:,
2271:,
2253:,
2231:MR
2229:,
2221:,
2213:,
2199:,
2185:,
2157:,
2151:,
2134:MR
2132:,
2120:,
2106:MR
2104:,
2090:,
2080:;
2064:,
2058:MR
2056:,
2046:,
2032:,
2022:;
2004:MR
2002:,
1992:,
1966:MR
1964:,
1956:,
1948:,
1938:,
1928:28
1926:,
1918:;
1905:MR
1903:,
1895:,
1887:,
1873:,
1849:MR
1847:.
1818:MR
1816:,
1806:,
1798:,
1771:.
1654:.
1459:A
1439:D(
1417:.
1288:F'
1267:.
477:.
360:.
59:,
38:.
2315::
2287::
2279::
2249::
2207::
2165::
2128::
2098::
2050::
2040::
1988::
1952::
1934::
1881::
1855:.
1843::
1802::
1769:A
1765:A
1757:A
1751:(
1730:R
1723:R
1719:C
1715:R
1711:T
1707:C
1703:C
1699:T
1681:k
1677:k
1669:k
1652:S
1648:R
1641:R
1637:S
1633:S
1629:R
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1613:(
1610:A
1605:B
1601:B
1597:A
1591:.
1589:T
1584:i
1582:T
1568:0
1560:n
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1524:0
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1500:T
1498:(
1493:A
1480:T
1473:T
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1465:A
1445:B
1441:A
1433:B
1429:A
1403:Y
1379:X
1367:B
1353:)
1348:Y
1343:,
1338:X
1333:(
1323:B
1319:B
1315:A
1308:B
1306:(
1304:0
1300:A
1298:(
1296:0
1294:K
1284:F
1280:B
1272:A
1255:B
1246:=
1241:Y
1219:A
1210:=
1205:T
1189:T
1168:)
1163:Y
1158:,
1153:X
1148:(
1128:)
1123:F
1118:,
1113:T
1108:(
1086:X
1062:F
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1006:T
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967:Y
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957:X
952:(
930:F
918:V
902:T
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876:0
870:V
864:M
858:U
852:0
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835:M
821:0
818:=
815:)
810:F
805:,
800:T
795:(
767:F
743:T
731:A
713:)
708:F
703:,
698:T
693:(
683:B
669:)
662:G
658:(
649:=
644:Y
622:)
619:G
616:(
607:=
602:X
590:A
576:)
569:F
565:(
556:=
551:T
529:)
526:F
523:(
514:=
509:F
497:B
493:A
467:G
459:F
455:T
449:1
438:T
434:B
429:G
425:T
423:(
418:A
406:T
404:(
401:A
396:F
392:T
390:(
387:A
382:B
378:A
374:T
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354:A
343:B
339:B
335:A
331:A
323:T
317:1
307:T
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298:T
296:(
291:A
283:T
281:(
278:A
269:B
265:T
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259:(
256:A
251:B
242:.
240:T
228:A
224:A
217:T
215:,
213:T
211:(
206:A
195:.
177:T
166:T
161:-
159:A
140:A
20:)
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