29:
2297:
George
Lusztig pushed this connection much further and was able to describe most of the characters of finite groups of Lie type in terms of representation theory of Hecke algebras. This work used a mixture of geometric techniques and various reductions, led to introduction of various objects
1699:
1358:. Moreover, extending earlier results of Benson and Curtis, George Lusztig provided an explicit isomorphism between the Hecke algebra and the group algebra after the extension of scalars to the quotient field of
2179:
I think it would be most appropriate to call it the
Iwahori algebra, but the name Hecke ring (or algebra) given by Iwahori himself has been in use for almost 20 years and it is probably too late to change it
562:
1156:
2278:, allowing them to complete the classification in the general linear case. Many of the techniques can be extended to other reductive groups, which remains an area of active research. It has been
773:
Since in
Coxeter groups with single laced Dynkin diagrams (for example Coxeter groups of type A and D) every pair of Coxeter generators is conjugated, the above-mentioned restriction of
1060:
1521:
984:
1845:
1567:
1809:
58:
799:
forces the multiparameter and the one-parameter Hecke algebras to be equal. Therefore, it is also very common to only look at one-parameter Hecke algebras.
635:
multiparameter Hecke algebra. This algebra is universal in the sense that every other multiparameter Hecke algebra can be obtained from it via the (unique)
2290:
It follows from
Iwahori's work that complex representations of Hecke algebras of finite type are intimately related with the structure of the spherical
1581:
1921:
2326:
2313:
Representation theory of affine Hecke algebras was developed by
Lusztig with a view towards applying it to description of representations of
2260:
over local fields in terms of appropriately constructed Hecke algebras. (Important contributions were also made by Joseph
Bernstein and
2475:
2433:
2412:
2391:
2353:
1942:
80:
1898:
457:
2291:
1370:
1077:
2495:
17:
932:
may be permitted as well. For technical reasons it is also often convenient only to consider positive weight functions.
153:
2306:
of Hecke algebras and representations at roots of unity turned out to be related with the theory of canonical bases in
41:
51:
45:
37:
2375:
2317:-adic groups. It is different in many ways from the finite case. A generalization of affine Hecke algebras, called
2274:
2190:
62:
1406:
1351:
269:
1009:
1247:
3. Elements of the natural basis are invertible. For example, from the quadratic relation we conclude that
1063:
2303:
1380:
701:
1478:
943:
2307:
2230:
1926:
Iwahori–Hecke algebras first appeared as an important special case of a very general construction in
1818:
1540:
1465:
1965:
1301:
339:
1328:
1316:
261:
222:
2282:
that all Hecke algebras that are ever needed are mild generalizations of affine Hecke algebras.
1785:
605:
in our notation). While this does not change the general theory, many formulae look different.
454:: in later books and papers, Lusztig used a modified form of the quadratic relation that reads
2490:
2471:
2429:
2408:
2387:
2349:
2261:
2222:
1908:
in
Coxeter groups are defined through the behavior of the canonical basis under the action of
636:
129:
110:
2361:
On some Bruhat decomposition and the structure of the Hecke rings of p-adic
Chevalley groups.
2450:
2214:
2060:
1939:
200:
149:
137:
2467:
2446:
2425:
2404:
2383:
2368:
2345:
2464:
2443:
2422:
2401:
2380:
2365:
2342:
2257:
2113:
2098:
1969:
1237:
1163:
1323:
is specialized to any complex number outside of an explicitly given list (consisting of
2322:
2265:
2129:
1436:
1324:
1308:
177:
2418:
762:
respectively), then one obtains the so-called generic one-parameter Hecke algebra of (
2484:
2454:
2397:
2359:
2298:
generalizing Hecke algebras and detailed understanding of their representations (for
2269:
2238:
141:
133:
125:
118:
2248:
Work of Roger Howe in the 1970s and his papers with Allen Moy on representations of
1991:), can be endowed with a structure of an associative algebra under the operation of
1354:
zero, then the one-parameter Hecke algebra is a semisimple associative algebra over
2117:
2102:
2072:
1927:
1770:
1429:
1312:
1297:
883:)), then a common specialization to look at is the one induced by the homomorphism
145:
2256:) opened a possibility of classifying irreducible admissible representations of
2194:
1992:
999:
106:
94:
2379:, Cambridge tracts in mathematics, vol. 163. Cambridge University Press, 2005.
1694:{\displaystyle C'_{w}=\left(q^{-1/2}\right)^{l(w)}\sum _{y\leq w}P_{y,w}T_{y},}
2279:
2152:
1949:
577:
114:
2463:, Annals of Mathematics Studies, vol. 129, Princeton University Press, 1993.
2059:) then the Hecke ring is commutative and its representations were studied by
1375:
A great discovery of
Kazhdan and Lusztig was that a Hecke algebra admits a
2421:, University Lecture Series, vol.15, American Mathematical Society, 1999.
905:
If one uses the convention with half-integer powers, then weight function
2339:
2170:, the cardinality of the finite field. George Lusztig remarked in 1984 (
2400:, CRM monograph series, vol.18, American Mathematical Society, 2003.
2221:. The resulting Hecke ring is isomorphic to the Hecke algebra of the
2108:
The case leading to the Hecke algebra of a finite Weyl group is when
1464:. It can further be proved that this automorphism is involutive (has
2419:
Iwahori-Hecke algebras and Schur algebras of the symmetric group
2364:
Publications Mathématiques de l'IHÉS, 25 (1965), pp. 5–48.
1573:
and if one writes its expansion in terms of the natural basis:
564:
After extending the scalars to include the half-integer powers
22:
2340:
Group
Characters, Symmetric Functions, and the Hecke Algebra
1832:
1554:
557:{\displaystyle (T_{s}-q_{s}^{1/2})(T_{s}+q_{s}^{-1/2})=0.}
2376:
Linear and projective representations of symmetric groups
1904:
The Kazhdan–Lusztig notions of left, right and two-sided
2075:
then the resulting algebra turns out to be commutative.
1151:{\displaystyle T_{w}=T_{s_{1}}T_{s_{2}}\ldots T_{s_{n}}}
140:. Representations of Hecke algebras led to discovery of
16:
For other mathematical rings called Hecke algebras, see
2461:
The admissible dual of GL(n) via compact open subgroups
2185:
Iwahori and Matsumoto (1965) considered the case when
1158:. This basis of Hecke algebra is sometimes called the
1821:
1788:
1584:
1543:
1481:
1327:), then the resulting one-parameter Hecke algebra is
1080:
1012:
946:
460:
132:. This connection found a spectacular application in
2105:, which gave the name to Hecke algebras in general.
2172:Characters of reductive groups over a finite field
1839:
1803:
1693:
1561:
1515:
1150:
1054:
978:
556:
1886:} is obtained in a similar way. The polynomials
50:but its sources remain unclear because it lacks
2237:has been specialized to the cardinality of the
723:) as constructed above. One calls this process
1335:(which also corresponds to the specialization
2144:) is obtained from the generic Hecke algebra
990:indexed by the elements of the Coxeter group
807:If an integral weight function is defined on
8:
1897:) making appearance in this theorem are the
1331:and isomorphic to the complex group algebra
152:proposed Hecke algebras as a foundation for
2264:.) These ideas were taken much further in
1386:The generic multiparameter Hecke algebra,
1831:
1826:
1820:
1787:
1682:
1666:
1650:
1631:
1617:
1610:
1589:
1583:
1553:
1548:
1542:
1501:
1491:
1486:
1480:
1184:2. The elements of the natural basis are
1140:
1135:
1120:
1115:
1103:
1098:
1085:
1079:
1046:
1033:
1023:
1011:
964:
954:
945:
535:
528:
523:
510:
490:
486:
481:
468:
459:
81:Learn how and when to remove this message
2442:, J. Algebra 71 (1981), no. 2, 490–498.
1922:Hecke algebra of a locally compact group
1916:Hecke algebra of a locally compact group
1569:which is invariant under the involution
1055:{\displaystyle w=s_{1}s_{2}\ldots s_{n}}
735:If one specializes every indeterminate
580:to the previously defined one (but the
2398:Hecke algebras with unequal parameters
2358:Iwahori, Nagayoshi; Matsumoto, Hideya
1439:with respect to the bar involution of
1346:is a finite group and the ground ring
2132:. Iwahori showed that the Hecke ring
609:Generic Multiparameter Hecke Algebras
7:
2327:Macdonald's constant term conjecture
2459:Colin Bushnell and Philip Kutzko,
2162:by specializing the indeterminate
2097:) we get the abstract ring behind
676:-algebra and the scalar extension
14:
2440:On a theorem of Benson and Curtis
2286:Representations of Hecke algebras
1943:locally compact topological group
1729:has degree less than or equal to
1383:of a variety of related objects.
940:1. The Hecke algebra has a basis
2292:principal series representations
1516:{\displaystyle T_{w^{-1}}^{-1}.}
979:{\displaystyle (T_{w})_{w\in W}}
278:(and the above restriction that
160:Hecke algebras of Coxeter groups
27:
1840:{\displaystyle C_{w}^{\prime }}
1562:{\displaystyle C_{w}^{\prime }}
1379:basis, which in a way controls
1170:corresponds to the identity of
898:is a single indeterminate over
576:the resulting Hecke algebra is
164:Start with the following data:
154:topological quantum computation
1641:
1635:
1537:there exists a unique element
961:
947:
545:
503:
500:
461:
18:Hecke algebra (disambiguation)
1:
1995:. This algebra is denoted by
646:which maps the indeterminate
312:Multiparameter Hecke Algebras
2455:10.1016/0021-8693(81)90188-5
2294:of finite Chevalley groups.
1938:) be a pair consisting of a
1855:form a basis of the algebra
731:One-parameter Hecke Algebras
318:multiparameter Hecke algebra
2319:double affine Hecke algebra
1899:Kazhdan–Lusztig polynomials
1300:and the ground ring is the
803:Coxeter groups with weights
2512:
2233:, where the indeterminate
2189:is a group of points of a
1919:
1527:Kazhdan - Lusztig Theorem:
1371:Kazhdan–Lusztig polynomial
1368:
1319:that if the indeterminate
742:to a single indeterminate
668:. This homomorphism turns
113:, is a deformation of the
15:
2213:is what is now called an
2191:reductive algebraic group
2166:of the latter algebra to
1804:{\displaystyle y\nleq w.}
404:< ∞ factors and
397:..., where each side has
300:are conjugated), that is
1420:and acts as identity on
727:of the generic algebra.
180:with the Coxeter matrix
36:This article includes a
2304:Modular representations
2193:over a non-archimedean
1706:one has the following:
138:new invariants of knots
65:more precise citations.
2302:not a root of unity).
1859:, which is called the
1841:
1813:
1805:
1695:
1563:
1517:
1342:5. More generally, if
1152:
1056:
980:
746:over the integers (or
702:canonically isomorphic
558:
128:of the group rings of
2496:Representation theory
2373:Alexander Kleshchev,
2308:affine quantum groups
2063:. More generally if (
1863:of the Hecke algebra
1842:
1806:
1696:
1564:
1524:
1518:
1428:admits a unique ring
1381:representation theory
1240:on the Coxeter group
1153:
1064:reduced decomposition
1057:
981:
704:to the Hecke algebra
559:
99:Iwahori–Hecke algebra
2325:in his proof of the
2231:affine Hecke algebra
1966:continuous functions
1960:. Then the space of
1861:dual canonical basis
1819:
1786:
1582:
1541:
1479:
1078:
1010:
944:
587:here corresponds to
458:
2310:and combinatorics.
1836:
1597:
1558:
1509:
1468:two) and takes any
544:
499:
416:Quadratic Relation:
262:Laurent polynomials
124:Hecke algebras are
2338:David Goldschmidt
1837:
1822:
1801:
1691:
1661:
1585:
1559:
1544:
1513:
1482:
1148:
1052:
976:
795:are conjugated in
554:
519:
477:
136:' construction of
130:Artin braid groups
38:list of references
2438:Lusztig, George,
2262:Andrey Zelevinsky
2223:affine Weyl group
2174:, xi, footnote):
2101:in the theory of
2007:) and called the
1646:
994:. In particular,
637:ring homomorphism
251:are conjugate in
221:} is a family of
111:Nagayoshi Iwahori
91:
90:
83:
2503:
2396:George Lusztig,
2258:reductive groups
2215:Iwahori subgroup
2061:Ian G. Macdonald
1846:
1844:
1843:
1838:
1835:
1830:
1810:
1808:
1807:
1802:
1744:
1742:
1741:
1738:
1735:
1700:
1698:
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1692:
1687:
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1676:
1660:
1645:
1644:
1630:
1626:
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1621:
1593:
1568:
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1565:
1560:
1557:
1552:
1522:
1520:
1519:
1514:
1508:
1500:
1499:
1498:
1463:
1462:
1292:4. Suppose that
1288:
1287:
1270:
1269:
1258:
1257:
1157:
1155:
1154:
1149:
1147:
1146:
1145:
1144:
1127:
1126:
1125:
1124:
1110:
1109:
1108:
1107:
1090:
1089:
1061:
1059:
1058:
1053:
1051:
1050:
1038:
1037:
1028:
1027:
985:
983:
982:
977:
975:
974:
959:
958:
928:
926:
925:
922:
919:
757:
756:
598:
597:
575:
574:
563:
561:
560:
555:
543:
539:
527:
515:
514:
498:
494:
485:
473:
472:
366:Braid Relations:
346:with generators
201:commutative ring
150:Michael Freedman
86:
79:
75:
72:
66:
61:this article by
52:inline citations
31:
30:
23:
2511:
2510:
2506:
2505:
2504:
2502:
2501:
2500:
2481:
2480:
2417:Andrew Mathas,
2335:
2288:
2275:theory of types
2208:
2150:
2114:Chevalley group
2099:Hecke operators
2058:
2041:
1977:
1970:compact support
1924:
1918:
1892:
1877:
1869:canonical basis
1817:
1816:
1784:
1783:
1781:
1739:
1736:
1733:
1732:
1730:
1724:
1715:
1678:
1662:
1606:
1602:
1601:
1580:
1579:
1539:
1538:
1487:
1477:
1476:
1473:
1461:
1456:
1455:
1454:
1448:
1391:
1373:
1367:
1365:Canonical basis
1309:complex numbers
1286:
1283:
1282:
1281:
1275:
1268:
1265:
1264:
1263:
1256:
1253:
1252:
1251:
1238:length function
1207:
1201:
1194:
1179:
1164:neutral element
1136:
1131:
1116:
1111:
1099:
1094:
1081:
1076:
1075:
1042:
1029:
1019:
1008:
1007:
960:
950:
942:
941:
938:
923:
920:
917:
916:
914:
888:
805:
785:
778:
755:
752:
751:
750:
740:
733:
709:
696:
681:
662:
651:
617:
611:
604:
596:
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592:
591:
585:
573:
570:
569:
568:
506:
464:
456:
455:
445:
438:
431:
402:
395:
391:
387:
380:
376:
372:
361:and relations:
351:
338:) is a unital,
324:
314:
290:
283:
276:
260:is the ring of
241:
234:
211:
192:
162:
87:
76:
70:
67:
56:
42:related reading
32:
28:
21:
12:
11:
5:
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2371:
2356:
2334:
2331:
2323:Ivan Cherednik
2321:, was used by
2287:
2284:
2266:Colin Bushnell
2204:
2183:
2182:
2148:
2130:Borel subgroup
2124:elements, and
2112:is the finite
2054:
2037:
1975:
1920:Main article:
1917:
1914:
1890:
1875:
1834:
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1485:
1471:
1457:
1446:
1389:
1369:Main article:
1366:
1363:
1352:characteristic
1350:is a field of
1325:roots of unity
1284:
1273:
1266:
1254:
1205:
1199:
1192:
1186:multiplicative
1177:
1143:
1139:
1134:
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1123:
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953:
949:
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934:
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804:
801:
783:
776:
753:
738:
732:
729:
725:specialization
707:
692:
679:
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649:
615:
610:
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594:
583:
571:
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389:
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378:
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349:
322:
313:
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288:
281:
274:
270:indeterminates
255:
239:
232:
209:
204:
203:with identity.
194:
188:
178:Coxeter system
161:
158:
142:quantum groups
89:
88:
46:external links
35:
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2270:Philip Kutzko
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2239:residue field
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2103:modular forms
2100:
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2020:
2018:
2014:
2011:of the pair (
2010:
2006:
2002:
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1994:
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1967:
1964:-biinvariant
1963:
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1815:The elements
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1483:
1474:
1467:
1460:
1453:
1449:
1442:
1438:
1434:
1431:
1427:
1423:
1419:
1415:
1411:
1408:
1404:
1400:
1396:
1392:
1384:
1382:
1378:
1372:
1364:
1362:
1361:
1357:
1353:
1349:
1345:
1340:
1338:
1334:
1330:
1326:
1322:
1318:
1314:
1310:
1306:
1303:
1299:
1295:
1290:
1280:
1276:
1262:
1250:
1245:
1243:
1239:
1235:
1231:
1227:
1223:
1219:
1215:
1211:
1204:
1198:
1191:
1187:
1182:
1180:
1173:
1169:
1165:
1161:
1160:natural basis
1141:
1137:
1132:
1128:
1121:
1117:
1112:
1104:
1100:
1095:
1091:
1086:
1082:
1073:
1069:
1065:
1047:
1043:
1039:
1034:
1030:
1024:
1020:
1016:
1013:
1005:
1003:
997:
993:
989:
971:
968:
965:
955:
951:
935:
933:
931:
912:
908:
903:
901:
897:
893:
889:
882:
878:
874:
870:
866:
862:
858:
854:
850:
846:
842:
838:
834:
830:
826:
822:
818:
814:
810:
802:
800:
798:
794:
790:
786:
779:
771:
769:
765:
761:
749:
745:
741:
730:
728:
726:
722:
718:
714:
710:
703:
699:
695:
690:
686:
682:
675:
671:
667:
663:
656:
652:
645:
641:
638:
634:
630:
626:
622:
618:
608:
606:
601:
590:
586:
579:
567:
551:
548:
540:
536:
532:
529:
524:
520:
516:
511:
507:
495:
491:
487:
482:
478:
474:
469:
465:
453:
446:
439:
432:
425:
421:
417:
414:
411:
407:
403:
396:
381:
367:
364:
363:
362:
360:
356:
352:
345:
343:
337:
333:
329:
325:
319:
311:
307:
303:
299:
295:
291:
284:
277:
271:
267:
263:
259:
256:
254:
250:
246:
242:
235:
228:
224:
220:
216:
212:
205:
202:
198:
195:
191:
187:
183:
179:
175:
171:
167:
166:
165:
159:
157:
155:
151:
147:
143:
139:
135:
134:Vaughan Jones
131:
127:
122:
120:
119:Coxeter group
116:
115:group algebra
112:
108:
105:, named for
104:
103:Hecke algebra
100:
96:
85:
82:
74:
64:
60:
54:
53:
47:
43:
39:
34:
25:
24:
19:
2460:
2439:
2374:
2360:
2318:
2314:
2312:
2299:
2296:
2289:
2273:
2253:
2249:
2247:
2242:
2234:
2226:
2218:
2210:
2205:
2201:
2197:
2186:
2184:
2178:
2171:
2167:
2163:
2159:
2155:
2145:
2141:
2137:
2133:
2125:
2121:
2118:finite field
2109:
2107:
2094:
2090:
2086:
2082:
2078:
2077:
2073:Gelfand pair
2068:
2064:
2055:
2051:
2047:
2043:
2038:
2034:
2030:
2026:
2022:
2021:
2016:
2012:
2008:
2004:
2000:
1996:
1988:
1984:
1980:
1973:
1961:
1957:
1953:
1945:
1935:
1931:
1928:group theory
1925:
1909:
1905:
1903:
1894:
1887:
1883:
1879:
1872:
1868:
1864:
1860:
1856:
1852:
1851:varies over
1848:
1814:
1776:
1771:Bruhat order
1766:
1762:
1758:
1754:
1750:
1746:
1726:
1719:
1710:
1705:
1570:
1534:
1530:
1526:
1525:
1469:
1458:
1451:
1444:
1440:
1432:
1430:automorphism
1425:
1421:
1417:
1413:
1409:
1402:
1398:
1394:
1387:
1385:
1376:
1374:
1359:
1355:
1347:
1343:
1341:
1336:
1332:
1320:
1313:Jacques Tits
1304:
1298:finite group
1293:
1291:
1278:
1271:
1260:
1248:
1246:
1241:
1236:denotes the
1233:
1229:
1225:
1221:
1217:
1213:
1209:
1202:
1196:
1189:
1185:
1183:
1175:
1171:
1167:
1159:
1071:
1067:
1001:
995:
991:
987:
939:
929:
910:
906:
904:
899:
895:
891:
884:
880:
876:
872:
868:
864:
860:
856:
852:
848:
844:
840:
836:
832:
828:
824:
820:
816:
812:
811:(i.e. a map
808:
806:
796:
792:
788:
781:
780:being equal
774:
772:
767:
763:
759:
747:
743:
736:
734:
724:
720:
716:
712:
705:
697:
693:
688:
684:
677:
673:
669:
665:
658:
657:to the unit
654:
647:
643:
639:
632:
628:
624:
620:
613:
612:
599:
588:
581:
565:
451:
450:
441:
434:
427:
423:
419:
415:
409:
405:
398:
383:
368:
365:
358:
354:
347:
341:
340:associative
335:
331:
327:
320:
317:
315:
305:
301:
297:
293:
286:
279:
272:
265:
257:
252:
248:
244:
237:
230:
226:
218:
214:
207:
196:
189:
185:
181:
173:
169:
163:
146:Michio Jimbo
123:
102:
98:
92:
77:
68:
57:Please help
49:
2280:conjectured
2195:local field
1993:convolution
107:Erich Hecke
95:mathematics
63:introducing
2485:Categories
2333:References
2200:, such as
2153:Weyl group
2009:Hecke ring
1940:unimodular
1437:semilinear
1412:that maps
1407:involution
1405:), has an
1329:semisimple
1188:, namely,
936:Properties
847:) for all
578:isomorphic
426:we have: (
408:belong to
229:such that
2252:-adic GL(
2229:, or the
1952:subgroup
1833:′
1793:≰
1655:≤
1648:∑
1612:−
1555:′
1529:For each
1503:−
1493:−
1443:and maps
1377:different
1232:), where
1208:whenever
1129:…
1040:…
969:∈
787:whenever
691:) ⊗
631:) is the
530:−
475:−
447:+ 1) = 0.
292:whenever
243:whenever
126:quotients
71:June 2020
2491:Algebras
2079:Example:
2023:Example:
1882:∈
1761:)−1) if
1595:′
1435:that is
1070:∈
894:, where
855:∈
664:∈
653:∈
418:For all
357:∈
353:for all
344:-algebra
217:∈
2468:1204652
2447:0630610
2426:1711316
2405:1974442
2384:2165457
2369:0185016
2346:1225799
2151:of the
2128:is its
2116:over a
2093:= SL(2,
2085:= SL(2,
2071:) is a
1930:. Let (
1769:in the
1743:
1731:
1424:. Then
1339:↦ 1) .
1074:, then
1004:-module
927:
915:
672:into a
633:generic
452:Warning
176:) is a
59:improve
2474:
2432:
2411:
2390:
2352:
2209:, and
2089:) and
2042:) and
1950:closed
1948:and a
1867:. The
1847:where
1782:=0 if
1317:proved
1162:. The
382:... =
97:, the
2120:with
2046:= SL(
2029:= SL(
1906:cells
1466:order
1302:field
1296:is a
1289:−1).
1181:= 1.
1062:is a
1006:. If
1000:free
998:is a
986:over
859:with
823:with
268:with
264:over
223:units
199:is a
117:of a
101:, or
44:, or
2472:ISBN
2430:ISBN
2409:ISBN
2388:ISBN
2350:ISBN
2268:and
2180:now.
1765:<
1315:has
791:and
316:The
296:and
247:and
109:and
2451:doi
2272:'s
2241:of
2225:of
2217:of
2158:of
2081:If
2025:If
2019:).
1968:of
1956:of
1891:y,w
1780:y,w
1725:in
1723:y,w
1716:=1,
1714:w,w
1475:to
1450:to
1416:to
1410:bar
1307:of
1277:+ (
1166:of
1066:of
770:).
758:to
700:is
422:in
406:s,t
225:of
184:= (
144:by
93:In
2487::
2470:,
2465:MR
2449:,
2444:MR
2428:,
2423:MR
2407:,
2402:MR
2386:,
2381:MR
2366:MR
2343:MR
2329:.
2245:.
2140://
2003://
1972:,
1912:.
1901:.
1878:|
1753:)−
1533:∈
1311:.
1259:=
1244:.
1224:)+
1216:)=
1214:yw
1193:yw
1174::
913:→
909::
902:.
890:↦
875:)+
867:)=
865:vw
839:)+
831:)=
829:vw
819:→
815::
642:→
552:0.
440:)(
433:−
401:st
304:=
285:=
236:=
213:|
193:),
190:st
172:,
156:.
148:.
121:.
48:,
40:,
2453::
2348:,
2315:p
2300:q
2254:n
2250:p
2243:K
2235:q
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2219:G
2211:K
2206:p
2202:Q
2198:K
2187:G
2168:p
2164:q
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2142:B
2138:G
2136:(
2134:H
2126:B
2122:p
2110:G
2095:Z
2091:K
2087:Q
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2069:K
2067:,
2065:G
2056:p
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2050:,
2048:n
2044:K
2039:p
2035:Q
2033:,
2031:n
2027:G
2017:K
2015:,
2013:G
2005:K
2001:G
1999:(
1997:H
1989:K
1987:/
1985:G
1983:\
1981:K
1979:(
1976:c
1974:C
1962:K
1958:G
1954:K
1946:G
1936:K
1934:,
1932:G
1910:H
1895:q
1893:(
1888:P
1884:W
1880:w
1876:w
1873:C
1871:{
1865:H
1857:H
1853:W
1849:w
1828:w
1824:C
1799:.
1796:w
1790:y
1777:P
1773:,
1767:w
1763:y
1759:y
1757:(
1755:l
1751:w
1749:(
1747:l
1745:(
1740:2
1737:/
1734:1
1727:Z
1720:P
1711:P
1689:,
1684:y
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1671:,
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1642:)
1639:w
1636:(
1633:l
1628:)
1623:2
1619:/
1615:1
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1604:(
1599:=
1591:w
1587:C
1571:i
1550:w
1546:C
1535:W
1531:w
1511:.
1506:1
1496:1
1489:w
1484:T
1472:w
1470:T
1459:s
1452:T
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1441:A
1433:i
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1399:S
1397:,
1395:W
1393:(
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1234:l
1230:w
1228:(
1226:l
1222:y
1220:(
1218:l
1212:(
1210:l
1206:w
1203:T
1200:y
1197:T
1195:=
1190:T
1178:e
1176:T
1172:H
1168:W
1142:n
1138:s
1133:T
1122:2
1118:s
1113:T
1105:1
1101:s
1096:T
1092:=
1087:w
1083:T
1072:W
1068:w
1048:n
1044:s
1035:2
1031:s
1025:1
1021:s
1017:=
1014:w
1002:A
996:H
992:W
988:A
972:W
966:w
962:)
956:w
952:T
948:(
930:Z
924:2
921:/
918:1
911:W
907:L
900:Z
896:q
892:q
887:s
885:q
881:w
879:(
877:l
873:v
871:(
869:l
863:(
861:l
857:W
853:w
851:,
849:v
845:w
843:(
841:L
837:v
835:(
833:L
827:(
825:L
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817:W
813:L
809:W
797:W
793:t
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777:s
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768:S
766:,
764:W
760:q
754:s
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717:S
715:,
713:W
711:(
708:R
706:H
698:R
694:A
689:S
687:,
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683:(
680:A
678:H
674:A
670:R
666:R
661:s
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629:q
627:,
625:S
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619:(
616:A
614:H
603:s
600:T
595:s
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584:s
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572:s
566:q
549:=
546:)
541:2
537:/
533:1
525:s
521:q
517:+
512:s
508:T
504:(
501:)
496:2
492:/
488:1
483:s
479:q
470:s
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462:(
444:s
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437:s
435:q
430:s
428:T
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412:.
410:S
399:m
394:t
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336:q
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249:t
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206:{
197:R
186:m
182:M
174:S
170:W
168:(
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78:(
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69:(
55:.
20:.
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