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

Abstract

If Z Z is the centre of the Lie algebra L L , its cohomology H ∗ ( L ) H^*(L) is naturally a module over the exterior algebra Λ Z \Lambda Z . Under suitable hypotheses on L L , motivated by recent work by Pouseele and Tirao, we find free summands in H ∗ ( L ) H^*(L) for this module structure, thus establishing the Toral Rank Conjecture for a new class of Lie algebras.