Free submodules for the central representation in the cohomology of Lie algebras
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- by Grant Cairns and Barry Jessup PDF
- Proc. Amer. Math. Soc. 136 (2008), 1919-1923 Request permission
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.References
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Additional Information
- Grant Cairns
- Affiliation: Department of Mathematics, La Trobe University, Melbourne, Australia 3086
- MR Author ID: 44265
- ORCID: 0000-0002-9011-4567
- Email: G.Cairns@latrobe.edu.au
- Barry Jessup
- Affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada K1N6N5
- MR Author ID: 265531
- Email: bjessup@uottawa.ca
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 1919-1923
- MSC (2000): Primary 17B55, 17B56; Secondary 55P62
- DOI: https://doi.org/10.1090/S0002-9939-08-09250-2
- MathSciNet review: 2383497