Pestov, Sviatoslav2013-11-072013-11-0720082008Source: Masters Abstracts International, Volume: 48-01, page: 0430.http://hdl.handle.net/10393/28015http://dx.doi.org/10.20381/ruor-19039The exterior algebra over the centre of a Lie algebra acts on the cohomology of the Lie algebra in a natural way. Focusing on nilpotent Lie algebras, we explore the module structure afforded by this action. We show that for all two-step nilpotent Lie algebras, this module structure is non-trivial, which partially answers a conjecture of Cairns and Jessup [4]. The presence of free submodules indicates that the Lie algebra satisfies Halperin's Toral rank conjecture [11]. We prove that two specific classes of two-step nilpotent Lie algebras enjoy cohomology spaces with free submodules.68 p.enMathematics.Thesis