Rota-Baxter operators on groups
Group Theory
2025-08-20 v2
Abstract
Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter operator on a group. We provide some general constructions of Rota-Baxter operators on a group. Given a map on a group, we study its extensions to a Rota-Baxter operator. We state the connection between Rota-Baxter operators on a group and Rota-Baxter operators on an associated Lie ring. We describe Rota-Baxter operators on sporadic simple groups.
Keywords
Cite
@article{arxiv.2103.01848,
title = {Rota-Baxter operators on groups},
author = {Valeriy G. Bardakov and Vsevolod Gubarev},
journal= {arXiv preprint arXiv:2103.01848},
year = {2025}
}
Comments
26 p; v2: formulation of Theorem 10.1 is corrected