Affine structures on groups and semi-braces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909598113333248 |
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| author | Stefanelli, Paola |
| author_facet | Stefanelli, Paola |
| contents | We introduce affine structures on groups and show they form a category equivalent to that of semi-braces. In particular, such a new description of semi-braces includes that presented by Rump for braces. By specific affine structures, we provide several instances of bi-skew braces, including some that are not $λ$-homomorphic. Finally, we give a method for determining affine structures on the Zappa product of two groups both endowed with affine structures and prove that such a construction allows for obtaining semi-braces that are not matched product of semi-braces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05000 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Affine structures on groups and semi-braces Stefanelli, Paola Group Theory Quantum Algebra 16T25, 81R50, 20M18 We introduce affine structures on groups and show they form a category equivalent to that of semi-braces. In particular, such a new description of semi-braces includes that presented by Rump for braces. By specific affine structures, we provide several instances of bi-skew braces, including some that are not $λ$-homomorphic. Finally, we give a method for determining affine structures on the Zappa product of two groups both endowed with affine structures and prove that such a construction allows for obtaining semi-braces that are not matched product of semi-braces. |
| title | Affine structures on groups and semi-braces |
| topic | Group Theory Quantum Algebra 16T25, 81R50, 20M18 |
| url | https://arxiv.org/abs/2207.05000 |