Malcev Yang-Baxter equation, weighted $\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras
Abstract
The purpose of this paper is to study the -operators on Malcev algebras and discuss the solutions of Malcev Yang-Baxter equation by -operators. Furthermore we introduce the notion of weighted -operators on Malcev algebras, which can be characterized by graphs of the semi-direct product Malcev algebra. Then we introduce a new algebraic structure called post-Malcev algebras. Therefore, post-Malcev algebras can be viewed as the underlying algebraic structures of weighted -operators on Malcev algebras. A post-Malcev algebra also gives rise to a new Malcev algebra. Post-Malcev algebras are analogues for Malcev algebras of post-Lie algebras and fit into a bigger framework with a close relationship with post-alternative algebras.
Keywords
Cite
@article{arxiv.2206.03629,
title = {Malcev Yang-Baxter equation, weighted $\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras},
author = {F. Harrathi and S. Mabrouk and O. Ncib and S. Silvestrov},
journal= {arXiv preprint arXiv:2206.03629},
year = {2022}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1312.5710, arXiv:2007.10939 by other authors