Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Articles in press \| Recently posted articles \| Most recent issue \| All issues

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
Retrieve article in: PDF
This article is available free of charge

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:

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


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS