On Leibniz Cohomology

Authors

Jorg Feldvoss, University of South AlabamaFollow
Friedrich Wagemann, University of Nantes, FranceFollow

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

Recommended Citation

Feldvoss, Jörg, and Friedrich Wagemann. "On Leibniz cohomology." Journal of Algebra 569 (2021): 276-317.