Category O for the Virasoro Algebra:: Cohomology and koszulity

被引：6

作者：

Boe, Brian D. ^{[1
]}

Nakano, Daniel K. ^{[1
]}

Wiesner, Emilie ^{[2
]}

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

[2] Ithaca Coll, Dept Math, Ithaca, NY 14850 USA

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2008年 / 234卷 / 01期

关键词：

virasoro algebra; Lie algebra cohomology; extensions;

D O I：

10.2140/pjm.2008.234.1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate blocks of the Category O for the Virasoro algebra over C. We demonstrate that the blocks have Kazhdan-Lusztig theories and that the truncated blocks give rise to interesting Koszul algebras. The simple modules have BGG resolutions, and from this we compute the extensions between Verma modules and simple modules, and between pairs of simple modules.

引用

页码：1 / 21

页数：21

共 27 条

[1]

BEILINSON A, 1981, CR ACAD SCI I-MATH, V292, P15

[2] Koszul duality patterns in representation theory [J].

Beilinson, A ;

Ginzburg, V ;

Soergel, W .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 9 (02) :473-527

[3]

Benson D.J., 1998, Representations and cohomology. I. Basic representation theory of finite groups and associative algebras, V30

[4]

BERNSTEIN I. N., 1971, LIE GROUPS THEIR REP, P21

[5]

Bernstein I. N., 1976, Funct. Anal. Appl., V10, P87

[6]

BOE BD, 2006, ARXIVMATHRT0604336

[7] KAZHDAN-LUSZTIG CONJECTURE AND HOLONOMIC SYSTEMS [J].

BRYLINSKI, JL ;

KASHIWARA, M .

INVENTIONES MATHEMATICAE, 1981, 64 (03) :387-410

[8] ABSTRACT KAZHDAN-LUSZTIG THEORIES [J].

CLINE, E ;

PARSHALL, B ;

SCOTT, L .

TOHOKU MATHEMATICAL JOURNAL, 1993, 45 (04) :511-534

[9]

CLINE E, 1988, J REINE ANGEW MATH, V391, P85

[10] On Ext-transfer for algebraic groups [J].

Cline, E ;

Parshall, B ;

Scott, L .

TRANSFORMATION GROUPS, 2004, 9 (03) :213-236

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