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Leibniz cohomologyChevalley-Eilenberg cohomologySpectral sequenceCohomological vanishingInvariant symmetric bilinear formCartan-Koszul mapComplete Lie algebraRigid Leibniz algebraWitt algebraBorel subalgebraParabolic subalgebraSemi-simple Leibniz algebraSecond Whitehead lemmaOuter derivation
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On Leibniz Cohomology, Jorg Feldvoss, Friedrich Wagemann
On Leibniz Cohomology, Jorg Feldvoss, Friedrich Wagemann
University Faculty and Staff Publications
In this paper we prove the Leibniz analogue of Whitehead's vanishing theorem for the Chevalley-Eilenberg cohomology of Lie algebras. As a consequence, we obtain the second Whitehead lemma for Leibniz algebras. Moreover, we compute the cohomology of several Leibniz algebras with ad joint or irreducible coefficients. Our main tool is a Leibniz analogue of the Hochschild-Serre spectral sequence, which is an extension of the dual of a spectral sequence of Pirashvili for Leibniz homology from symmetric bimodules to arbitrary bimodules.