Extensions and automorphisms of Rota-Baxter groups
Group Theory
2024-09-24 v1
Abstract
The notion of Rota-Baxter groups was recently introduced by Guo, Lang and Sheng [{\em Adv. Math.} 387 (2021), 107834, 34 pp.] in the geometric study of Rota-Baxter Lie algebras. They are closely related to skew braces as observed by Bardakov and Gubarev. In this paper, we study extensions of Rota-Baxter groups by constructing suitable cohomology theories. Among others, we find relations with the extensions of skew braces. Given an extension of Rota-Baxter groups, we also construct a short exact sequence connecting various automorphism groups, which generalizes the Wells short exact sequence.
Keywords
Cite
@article{arxiv.2212.06429,
title = {Extensions and automorphisms of Rota-Baxter groups},
author = {Apurba Das and Nishant Rathee},
journal= {arXiv preprint arXiv:2212.06429},
year = {2024}
}
Comments
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