English

On Leibniz cohomology

Algebraic Topology 2021-01-11 v4 Rings and Algebras

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 adjoint 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.

Keywords

Cite

@article{arxiv.1902.06128,
  title  = {On Leibniz cohomology},
  author = {Jörg Feldvoss and Friedrich Wagemann},
  journal= {arXiv preprint arXiv:1902.06128},
  year   = {2021}
}

Comments

We correct here an error in an earlier version

R2 v1 2026-06-23T07:42:41.623Z