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On the cohomology of a class of nilpotent Lie algebras

Published online by Cambridge University Press:  17 April 2009

Grant F. Armstrong  and
Stefan Sigg
Grant F. Armstrong
Affiliation:
School of Mathematics, La Trobe University, Melbourne Vic 3083, Australia, e-mail: matgfa@lure.latrobe.edu.au
Stefan Sigg
Affiliation:
Barlachstr. 1, D-69226 Nussloch, Germany, e-mail: stefan.sigg@sap-ag.de
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Abstract

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Let g denote a finite dimensional nilpotent Lie algebra over ℂ containing an Abelian ideal a of codimension 1, with z ∈ g/a. We give a combinatorial description of the Betti numbers of g in terms of the Jordan decomposition induced by ad(z)|a. As an application we prove that the filiform-nilpotent Lie algebras arising in the case t = 1 have unimodal Betti numbers.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 3 , December 1996 , pp. 517 - 527
Copyright
Copyright © Australian Mathematical Society 1996

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