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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
DOI: https://doi.org/10.1090/S0002-9939-99-04562-1
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 [Enhancements On Off] (What's this?)

  • 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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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: https://doi.org/10.1090/S0002-9939-99-04562-1
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

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