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Title: On the homology of free Lie algebras (English)
Author: Popescu, Calin
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 39
Issue: 4
Year: 1998
Pages: 661-669
Category: math
Summary: Given a principal ideal domain $R$ of characteristic zero, containing $1/2$, and a connected differential non-negatively graded free finite type $R$-module $V$, we prove that the natural arrow $ \Bbb{L} {F\kern -0.8pt H}(V) \rightarrow {F\kern -0.8pt H} \Bbb{L} (V)$ is an isomorphism of graded Lie algebras over $R$, and deduce thereby that the natural arrow ${U\kern -1pt F\kern -0.8pt H}\Bbb{L} (V) \rightarrow {F\kern -0.8pt H\kern -0.4pt U} \Bbb{L} (V)$ is an isomorphism of graded cocommutative Hopf algebras over $R$; as usual, $F$ stands for free part, $H$ for homology, $\Bbb{L}$ for free Lie algebra, and $U$ for universal enveloping algebra. Related facts and examples are also considered. (English)
Keyword: differential graded Lie algebra
Keyword: free Lie algebra on a differential graded module
Keyword: universal enveloping algebra
MSC: 17B01
MSC: 17B35
MSC: 17B55
MSC: 17B70
idZBL: Zbl 1059.17503
idMR: MR1715456
Date available: 2009-01-08T18:47:18Z
Last updated: 2012-04-30
Stable URL:
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