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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lie algebras of cohomological codimension one
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by Grant F. Armstrong, Grant Cairns and Gunky Kim PDF
Proc. Amer. Math. Soc. 127 (1999), 709-714 Request permission

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
  • MR Author ID: 44265
  • ORCID: 0000-0002-9011-4567
  • Email: G.Cairns@latrobe.edu.au
  • Gunky Kim
  • Affiliation: School of Mathematics, La Trobe University, Melbourne, Australia 3083
  • Email: G.Kim@latrobe.edu.au
  • Received by editor(s): May 13, 1997
  • Received by editor(s) in revised form: July 7, 1997
  • Communicated by: Roe Goodman
  • © Copyright 1999 American Mathematical Society
  • 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