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Explicit Betti numbers for a family of nilpotent Lie algebras

Author(s): Grant F. Armstrong; Grant Cairns; Barry Jessup
Journal: Proc. Amer. Math. Soc. 125 (1997), 381-385.
MSC (1991): Primary 17B56; Secondary 17B30, 22E40
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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:

1.
B.Cenkl and R.Porter, Cohomology of nilmanifolds, Algebraic Topology-Rational Homotopy (Y.Felix, eds.), Lecture Notes in Mathematics, vol. 1318, Springer-Verlag, Berlin and New York, 1988, pp. 73-86. MR 89i:57018

2.
J.Dixmier, Cohomologie des algèbres de Lie nilpotentes, Acta Sci. Math. Szeged 16 (1955), 246-250. MR 17:645b

3.
P.Griffiths and J.Morgan, Rational Homotopy Theory and Differential Forms, Progress in Mathematics, vol. 16, Birkhäuser, Boston, Basel, Stuttgart, 1981, pp. 73-86. MR 82m:55014

4.
K.Nomizu, On the cohomology of compact homogeneous spaces of nilpotent Lie groups, Annals of Math. 59 (1954), 531-538. MR 16:219c

5.
L.J.Santharoubane, Cohomology of Heisenberg Lie algebras, Proc. Amer. Math. Soc. 87 (1983), 23-28. MR 87b:17010

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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: matgc@lure.latrobe.edu.au

Barry Jessup
Affiliation: Department of Mathematics, University of Ottawa, Ottawa, Canada K1N 6N5
Email: bjessup@sciences.uottawa.ca

DOI: 10.1090/S0002-9939-97-03607-1
PII: S 0002-9939(97)03607-1
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
Copyright of article: Copyright 1997, American Mathematical Society

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The following works have cited this article

Cairns, Grant; Jessup, Barry; Pitkethly, Jane, On the Betti numbers of nilpotent Lie algebras of small dimension, Integrable systemsand foliations/Feuilletages et systèmes intégrables (Montpellier, 1995), Birkhäuser, Boston, 1997, pp. 19--31. MR 98c:17018

G.Armstrong and S.Sigg, On the cohomology of nilpotent Lie algebras containing an abelian ideal ofcodimension one, Bull. Austral. Math. Soc. 54 (1996), 517--527. (English)

G.Armstrong, Unimodal Betti numbers for a class of nilpotent Lie algebras, Comm. Algebra 25 (1997), 1893--1915.

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