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Explicit Betti numbers for a family
of nilpotent Lie algebras

Authors: Grant F. Armstrong, Grant Cairns and Barry Jessup
Journal: Proc. Amer. Math. Soc. 125 (1997), 381-385
MSC (1991): Primary 17B56; Secondary 17B30, 22E40
MathSciNet review: 1353371
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Abstract | References | Similar Articles | Additional Information

Abstract: Betti numbers for the Heisenberg Lie algebras were calculated by Santharoubane in his 1983 paper. However few other examples have appeared in the literature. In this note we give the Betti numbers for a family of $(2n+1)$-dimensional 2-step nilpotent extensions of $\mathbb {R}$ by ${\mathbb {R}}^{2n}$.

References [Enhancements On Off] (What's this?)

  • 1. Bohumil Cenkl and Richard Porter, Cohomology of nilmanifolds, Algebraic topology—rational homotopy (Louvain-la-Neuve, 1986) Lecture Notes in Math., vol. 1318, Springer, Berlin, 1988, pp. 73–86. MR 952572, 10.1007/BFb0077795
  • 2. J. Dixmier, Cohomologie des algèbres de Lie nilpotentes, Acta Sci. Math. Szeged 16 (1955), 246–250 (French). MR 0074780
  • 3. Phillip A. Griffiths and John W. Morgan, Rational homotopy theory and differential forms, Progress in Mathematics, vol. 16, Birkhäuser, Boston, Mass., 1981. MR 641551
  • 4. Katsumi Nomizu, On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Ann. of Math. (2) 59 (1954), 531–538. MR 0064057
  • 5. I. B. Frenkel, Representations of Kac-Moody algebras and dual resonance models, Applications of group theory in physics and mathematical physics (Chicago, 1982) Lectures in Appl. Math., vol. 21, Amer. Math. Soc., Providence, RI, 1985, pp. 325–353. MR 789298

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Additional Information

Grant F. Armstrong
Affiliation: School of Mathematics, La Trobe University, Melbourne, Australia 3083

Grant Cairns

Barry Jessup
Affiliation: Department of Mathematics, University of Ottawa, Ottawa, Canada K1N 6N5

Keywords: Lie algebra, nilpotent, cohomology
Received by editor(s): April 20, 1994
Received by editor(s) in revised form: August 31, 1995
Communicated by: Roe Goodman
Article copyright: © Copyright 1997 American Mathematical Society