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

Cairns, Grant; Jessup, Barry

doi:10.1090/S0002-9939-08-09250-2

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.

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