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arXiv · 2207.05000

Affine structures on groups and semi-braces

Paola Stefanelli
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Abstract

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 $\lambda$-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.

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Paola Stefanelli. 2022-07-11. Affine structures on groups and semi-braces. https://doi.org/10.1016/j.jpaa.2023.107383

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