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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lie algebras of cohomological codimension one


Authors: Grant F. Armstrong, Grant Cairns and Gunky Kim
Journal: Proc. Amer. Math. Soc. 127 (1999), 709-714
MSC (1991): Primary 17B56
MathSciNet review: 1469393
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Abstract: 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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Additional Information

Grant F. Armstrong
Affiliation: School of Mathematics, La Trobe University, Melbourne, Australia 3083
Email: matgfa@lure.latrobe.edu.au

Grant Cairns
Affiliation: School of Mathematics, La Trobe University, Melbourne, Australia 3083
Email: G.Cairns@latrobe.edu.au

Gunky Kim
Affiliation: School of Mathematics, La Trobe University, Melbourne, Australia 3083
Email: G.Kim@latrobe.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04562-1
PII: S 0002-9939(99)04562-1
Keywords: Lie algebra, cohomology, cohomological dimension
Received by editor(s): May 13, 1997
Received by editor(s) in revised form: July 7, 1997
Communicated by: Roe Goodman
Article copyright: © Copyright 1999 American Mathematical Society