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Uniconnected solutions to the Yang–Baxter equation arising from self-maps of groups
Canadian Mathematical Bulletin ( IF 0.6 ) Pub Date : 2021-04-20 , DOI: 10.4153/s0008439521000230
Wolfgang Rump 1
Affiliation  

Set-theoretic solutions to the Yang–Baxter equation can be classified by their universal coverings and their fundamental groupoids. Extending previous results, universal coverings of irreducible involutive solutions are classified in the degenerate case. These solutions are described in terms of a group with a distinguished self-map. The classification in the nondegenerate case is simplified and compared with the description in the degenerate case.



中文翻译:

由组的自映射产生的杨-巴克斯特方程的单连通解

Yang-Baxter 方程的集合论解可以通过它们的全覆盖和它们的基本群进行分类。扩展先前的结果,不可约对合解的普遍覆盖被归类为退化情况。这些解决方案是根据具有显着自映射的组来描述的。对非退化情况的分类进行了简化,并与退化情况下的描述进行了比较。

更新日期:2021-04-20
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