Nijenhuis operators on Leibniz algebras
Rings and Algebras
2023-06-14 v1
Abstract
In this paper, we study Nijenhuis operators on Leibniz algebras. We discuss the relationship of Nijenhuis operators with Rota-Baxter operators and modified Rota-Baxter operators on Leibniz algebras. We define a representation theory of Nijenhuis Leibniz algebras and construct a cohomology theory. Next, we define a one-parameter formal deformation theory of Nijenhuis Leibniz algebras and study infinitesimals, rigidity, and equivalences along the line of Gerstenhaber deformation theory. As an application of our cohomology theory, we show that our cohomology is deformation cohomology and study abelian extensions of such algebras.
Keywords
Cite
@article{arxiv.2306.06428,
title = {Nijenhuis operators on Leibniz algebras},
author = {Bibhash Mondal and Ripan Saha},
journal= {arXiv preprint arXiv:2306.06428},
year = {2023}
}
Comments
21 pages. arXiv admin note: text overlap with arXiv:2208.00560