Proceedings of the American Mathematical Society

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



Free submodules for the central representation in the cohomology of Lie algebras

Authors: Grant Cairns and Barry Jessup
Journal: Proc. Amer. Math. Soc. 136 (2008), 1919-1923
MSC (2000): Primary 17B55, 17B56; Secondary 55P62
Published electronically: February 7, 2008
MathSciNet review: 2383497
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Abstract: If $ Z$ is the centre of the Lie algebra $ L$, its cohomology $ H^*(L)$ is naturally a module over the exterior algebra $ \Lambda Z$. Under suitable hypotheses on $ L$, motivated by recent work by Pouseele and Tirao, we find free summands in $ H^*(L)$ for this module structure, thus establishing the Toral Rank Conjecture for a new class of Lie algebras.

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Additional Information

Grant Cairns
Affiliation: Department of Mathematics, La Trobe University, Melbourne, Australia 3086

Barry Jessup
Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada K1N6N5

Received by editor(s): October 25, 2006
Published electronically: February 7, 2008
Additional Notes: This research was supported in part by NSERC and the ARC
The second author would like to thank the members of the Department of Mathematics and Statistics at La Trobe University for their hospitality during his stay there
Communicated by: Paul Goerss
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.