Deformed solutions of the Yang-Baxter equation associated to dual weak left $\star$-braces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917288790196224 |
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| author | Wang, Shoufeng |
| author_facet | Wang, Shoufeng |
| contents | As generalizations of dual weak left braces and skew left braces, in this paper, dual weak left $\star$-braces and square skew left braces are introduced, respectively. We firstly show that a dual weak left $\star$-brace is exactly a strong semilattice of a family of square skew left braces. Then we introduce distributors for dual weak left $\star$-braces and prove that the map deformed by each distributor is always a solution of the Yang-Baxter equation. Our work may be regarded as extending and enriching some related results on skew left braces and weak left braces in literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19905 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deformed solutions of the Yang-Baxter equation associated to dual weak left $\star$-braces Wang, Shoufeng Group Theory Quantum Algebra 20M18, 16T25, 16Y99 As generalizations of dual weak left braces and skew left braces, in this paper, dual weak left $\star$-braces and square skew left braces are introduced, respectively. We firstly show that a dual weak left $\star$-brace is exactly a strong semilattice of a family of square skew left braces. Then we introduce distributors for dual weak left $\star$-braces and prove that the map deformed by each distributor is always a solution of the Yang-Baxter equation. Our work may be regarded as extending and enriching some related results on skew left braces and weak left braces in literature. |
| title | Deformed solutions of the Yang-Baxter equation associated to dual weak left $\star$-braces |
| topic | Group Theory Quantum Algebra 20M18, 16T25, 16Y99 |
| url | https://arxiv.org/abs/2602.19905 |