Inverse semi-braces and the Yang-Baxter equation
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916715860852736 |
|---|---|
| author | Catino, Francesco Mazzotta, Marzia Stefanelli, Paola |
| author_facet | Catino, Francesco Mazzotta, Marzia Stefanelli, Paola |
| contents | The main aim of this paper is to provide set-theoretical solutions of the Yang-Baxter equation that are not necessarily bijective, among these new idempotent ones. In the specific, we draw on both to the classical theory of inverse semigroups and to that of the most recently studied braces, to give a new research perspective to the open problem of finding solutions. Namely, we have recourse to a new structure, the inverse semi-brace, that is a triple $(S,+, \cdot)$ with $(S,+)$ a semigroup and $(S, \cdot)$ an inverse semigroup satisfying the relation $a \left(b + c\right) = a b + a\left(a^{-1} + c\right)$, for all $a,b,c \in S$, where $a^{-1}$ is the inverse of $a$ in $(S, \cdot)$. In particular, we give several constructions of inverse semi-braces which allow for obtaining solutions that are different from those until known. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_05730 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Inverse semi-braces and the Yang-Baxter equation Catino, Francesco Mazzotta, Marzia Stefanelli, Paola Quantum Algebra 16T25, 81R50, 16Y99, 16N20, 20M18 The main aim of this paper is to provide set-theoretical solutions of the Yang-Baxter equation that are not necessarily bijective, among these new idempotent ones. In the specific, we draw on both to the classical theory of inverse semigroups and to that of the most recently studied braces, to give a new research perspective to the open problem of finding solutions. Namely, we have recourse to a new structure, the inverse semi-brace, that is a triple $(S,+, \cdot)$ with $(S,+)$ a semigroup and $(S, \cdot)$ an inverse semigroup satisfying the relation $a \left(b + c\right) = a b + a\left(a^{-1} + c\right)$, for all $a,b,c \in S$, where $a^{-1}$ is the inverse of $a$ in $(S, \cdot)$. In particular, we give several constructions of inverse semi-braces which allow for obtaining solutions that are different from those until known. |
| title | Inverse semi-braces and the Yang-Baxter equation |
| topic | Quantum Algebra 16T25, 81R50, 16Y99, 16N20, 20M18 |
| url | https://arxiv.org/abs/2007.05730 |