On products of abelian skew braces
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911006997872640 |
|---|---|
| author | Ballester-Bolinches, A. Esteban-Romero, R. Pérez-Altarriba, P. |
| author_facet | Ballester-Bolinches, A. Esteban-Romero, R. Pérez-Altarriba, P. |
| contents | The main objective of this paper is to study factorisations of skew left braces through abelian subbraces. We prove a skew brace theoretical analog of the classical Itô's theorem about product of two abelian groups: if $B = A_1A_2$ is a skew brace which is the product of two abelian skew subbraces $A_1$ and $A_2$, and $A_1$ is a left and right ideal of $B$, then the commutator ideal $[B, B]^B$ of $B$ is an abelian brace. If $A_1$ is a left (non-necessarily right) ideal of $B$, we show that there exists a strong left ideal of $B$ contained in $A_1$ or $A_2$. We also show factorisations of relevant ideals of factorised braces that are sums and products of abelian subbraces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09844 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On products of abelian skew braces Ballester-Bolinches, A. Esteban-Romero, R. Pérez-Altarriba, P. Group Theory Quantum Algebra 16T25, 81R50, 20C35, 20C99, 20D40 The main objective of this paper is to study factorisations of skew left braces through abelian subbraces. We prove a skew brace theoretical analog of the classical Itô's theorem about product of two abelian groups: if $B = A_1A_2$ is a skew brace which is the product of two abelian skew subbraces $A_1$ and $A_2$, and $A_1$ is a left and right ideal of $B$, then the commutator ideal $[B, B]^B$ of $B$ is an abelian brace. If $A_1$ is a left (non-necessarily right) ideal of $B$, we show that there exists a strong left ideal of $B$ contained in $A_1$ or $A_2$. We also show factorisations of relevant ideals of factorised braces that are sums and products of abelian subbraces. |
| title | On products of abelian skew braces |
| topic | Group Theory Quantum Algebra 16T25, 81R50, 20C35, 20C99, 20D40 |
| url | https://arxiv.org/abs/2506.09844 |