Extensions and automorphisms of Rota-Baxter groups

Apurba Das; Nishant Rathee

doi:10.1016/j.jalgebra.2023.09.006

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arXiv · 2212.06429

Extensions and automorphisms of Rota-Baxter groups

Apurba Das·Nishant Rathee

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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.

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BibTeX RIS

Apurba Das, Nishant Rathee. 2022-12-13. Extensions and automorphisms of Rota-Baxter groups. https://doi.org/10.1016/j.jalgebra.2023.09.006

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