Lie algebras of cohomological codimension one

Lie algebras of cohomological codimension one

We show that if \mathfrak{g} is a finite dimensional real Lie algebra, then \mathfrak{g} has cohomological dimension cd(\mathfrak{g})=\dim (\mathfrak{g})-1 if and only if \mathfrak{g} is a unimodular extension of the two-dimensional non-Abelian Lie algebra \mathfrak{aff}.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society Vol. 127; no. 3; pp. 709 - 714
Main Authors: Armstrong, Grant F., Cairns, Grant, Kim, Gunky
Format: Journal Article
Language:English
Published: American Mathematical Society 01-03-1999
Subjects:
Adjoints
Algebra
Mathematical duality
Mathematical theorems
Subalgebras
cohomological dimension
Lie algebra
cohomology
Online Access:Get full text
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Description
Summary:We show that if \mathfrak{g} is a finite dimensional real Lie algebra, then \mathfrak{g} has cohomological dimension cd(\mathfrak{g})=\dim (\mathfrak{g})-1 if and only if \mathfrak{g} is a unimodular extension of the two-dimensional non-Abelian Lie algebra \mathfrak{aff}.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-99-04562-1