Document Type

Article

Publication Title

Journal of Algebra

Abstract

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.

First Page

276

Last Page

317

DOI

https://doi.org/10.1016/j.jalgebra.2020.11.003

Publication Date

3-2021

Department

Mathematics and Statistics

Comments

This is the pre-print version of this article. The published version can be found in the Journal of Algebra at this link:

https://doi.org/10.1016/j.jalgebra.2020.11.003

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