On the Generalized Enveloping Algebra of a Color Lie Algebra
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- 作者：Toukaiddine Petit (1)
Freddy Van Oystaeyen (1) - 关键词：Cohomology ; Universal enveloping algebra ; Generalized enveloping algebra ; Color Lie algebra ; 16E40 ; 17B35 ; 17B75
- 刊名：Algebras and Representation Theory
- 出版年：2007
- 出版时间：August 2007
- 年：2007
- 卷：10
- 期：4
- 页码：367-378
- 全文大小：410KB
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Freddy Van Oystaeyen (1)
1. Departement Wiskunde en Informatica, Universiteit Antwerpen, 2020, Antwerp, Belgium - ISSN：1572-9079
文摘
Let G be an abelian group, 蔚 an anti-bicharacter of G and L a G-graded 蔚 Lie algebra (color Lie algebra) over $\mathbb{K}$ a field of characteristic zero. We prove that for all G-graded, positively filtered A such that the associated graded algebra is isomorphic to the G-graded 蔚-symmetric algebra S(L), there is a G- graded 蔚-Lie algebra L and a G-graded scalar two cocycle $\omega\in\mathrm{Z}_{gr}^2(L,\mathbb{K})$ , such that A is isomorphic to U 蠅 (L) the generalized enveloping algebra of L associated with 蠅. We also prove there is an isomorphism of graded spaces between the Hochschild cohomology of the generalized universal enveloping algebra U(L) and the generalized cohomology of the color Lie algebra L.