Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Lie algebras of cohomological codimension one

Author(s): Grant F. Armstrong; Grant Cairns; 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 $\mathfrak{aff}$ .

References:

1.: J-J. Koszul, Homologie et cohomologie des algèbres de Lie, Bull. Soc. math. France 78 (1950), 65-127. MR 12:120g
2.: J. Milnor, Curvatures of left invariant metrics on Lie groups, Adv. in Math. 21 (1976), 293-329. MR 54:12970
3.: H. Tasaki and M. Umehara, An invariant on 3-dimensional Lie algebras, Proc. Amer. Math. Soc. 115 (1992), 293-294. MR 92i:17009

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