Pre-Leibniz algebras
Rings and Algebras
2022-02-08 v1 Representation Theory
Abstract
The notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elements are pre-Leibniz algebras. Using this characterization, we define the cohomology of a pre-Leibniz algebra with coefficients in a representation. This cohomology is shown to split the Loday-Pirashvili cohomology of Leibniz algebras. As applications of our cohomology, we study formal and finite order deformations of a pre-Leibniz algebra. Finally, we define homotopy pre-Leibniz algebras and classify some special types of homotopy pre-Leibniz algebras.
Cite
@article{arxiv.2202.03160,
title = {Pre-Leibniz algebras},
author = {Apurba Das},
journal= {arXiv preprint arXiv:2202.03160},
year = {2022}
}
Comments
16 pages