Hochschild cohomology and stratifying ideals

被引：28

作者：

Koenig, Steffen ^{[2
]}

Nagase, Hiroshi ^{[1
]}

机构：

[1] Nara Natl Coll Technol, Nara 6391080, Japan

[2] Univ Cologne, Math Inst, D-50931 Cologne, Germany

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2009年 / 213卷 / 05期

关键词：

ALGEBRAS; RING;

D O I：

10.1016/j.jpaa.2008.10.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Suppose B is an algebra with a stratifying ideal BeB generated by an idempotent e. We will establish long exact sequences relating the Hochschild cohomology groups of the three algebras B. B/BeB and eBe. This provides a common generalization of various known results, all of which extend Happel's long exact sequence for one-point extensions. Applying one of these sequences to Hochschild cohomology algebras modulo the ideal generated by homogeneous nilpotent elements shows, in some cases, that these algebras are finitely generated. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：886 / 891

页数：6

共 13 条

[1] Cartan H., 1973, PRINCETON LANDMARKS
[2] Cohomology of split algebras and of trivial extensions
Cibils, C
Marcos, E
Redondo, MJ
Solotar, A
[J]. GLASGOW MATHEMATICAL JOURNAL, 2003, 45 : 21 - 40
[3] Cline E, 1996, MEM AM MATH SOC, V124, P1
[4] de la Peña JA, 2006, TSUKUBA J MATH, V30, P61
[5] THE HOCHSCHILD COHOMOLOGY RING MODULO NILPOTENCE OF A MONOMIAL ALGEBRA
Green, Edward L.
Snashall, Nicole
Solberg, Oyvind
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2006, 5 (02) : 153 - 192
[6] The Hochschild cohomology ring of a selfinjective algebra of finite representation type
Green, EL
Snashall, N
Solberg, O
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (11) : 3387 - 3393
[7] GREEN EL, 2002, P 9 INT C BEIJ 2000, V2, P192
[8] Happel D., Lecture Notes in Mathematics, V1404, DOI DOI 10.1007/BFB0084073
[9] Holm T., 2000, Beitr. Algebra Geom., V41, P291
[10] A characteristic free approach to Brauer algebras
König, S
Xi, CC
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (04) : 1489 - 1505

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