A Wells-like exact sequence for abelian extensions of relative Rota--Baxter groups
Abstract
Relative Rota--Baxter groups, a generalization of Rota--Baxter groups, are closely connected to skew left braces, which play a fundamental role in understanding non-degenerate set-theoretical solutions to the Yang-Baxter equation. In this paper, we explore the inducibility problem for automorphisms of abelian extensions of relative Rota--Baxter groups. This problem is intricately linked to the recently introduced second cohomology of relative Rota--Baxter groups. Specifically, we prove a Wells-like exact sequence for abelian extensions of relative Rota--Baxter groups. The sequence establishes a connection among the group of derivations, certain automorphism group, and the second cohomology of relative Rota--Baxter groups, thereby giving precise structural relationships between these groups.
Keywords
Cite
@article{arxiv.2401.14058,
title = {A Wells-like exact sequence for abelian extensions of relative Rota--Baxter groups},
author = {Pragya Belwal and Nishant Rathee},
journal= {arXiv preprint arXiv:2401.14058},
year = {2024}
}
Comments
22 pages. arXiv admin note: text overlap with arXiv:2309.00692, arXiv:2311.12384