A Wells-like exact sequence for abelian extensions of relative Rota--Baxter groups
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| Format: | Preprint |
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2024
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| _version_ | 1866910307818930176 |
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| author | Belwal, Pragya Rathee, Nishant |
| author_facet | Belwal, Pragya Rathee, Nishant |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_14058 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Wells-like exact sequence for abelian extensions of relative Rota--Baxter groups Belwal, Pragya Rathee, Nishant Group Theory Quantum Algebra Rings and Algebras [2010]{17B38, 16T25, 81R50} 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. |
| title | A Wells-like exact sequence for abelian extensions of relative Rota--Baxter groups |
| topic | Group Theory Quantum Algebra Rings and Algebras [2010]{17B38, 16T25, 81R50} |
| url | https://arxiv.org/abs/2401.14058 |