Braces and the Yang–Baxter Equation
Braces and the Yang–Baxter Equation
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大括号和杨-巴克斯特方程
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
J. Okniński
中科院分区：
文献类型：
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作者：
F. Cedó;E. Jespers;J. Okniński
本文讨论了Yang-Baxter方程的大括号与非退化对合集论解的几个方面的关系，并得到了许多结论。特别地，对于每个正整数n，构造了具有多置换水平n和交换对合Yang-Baxter群的Yang-Baxter方程的有限无平方多置换解.这就回答了Gateva-Ivanova和卡梅隆的一个问题。证明了当对合Yang-Baxter群为交换群时，Yang-Baxter方程的有限个非退化对合集理论解是多置换解.早些时候，作者证明了这一点与额外的无平方假设的解决方案。证明了与左支撑相关的有限个无平方因子的非退化对合集合论解是多置换解。
Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation are discussed and many consequences are derived. In particular, for each positive integer n a finite square-free multipermutation solution of the Yang–Baxter equation with multipermutation level n and an abelian involutive Yang–Baxter group is constructed. This answers a problem of Gateva-Ivanova and Cameron. It is proved that finite non-degenerate involutive set-theoretic solutions of the Yang–Baxter equation whose associated involutive Yang–Baxter group is abelian are multipermutation solutions. Earlier the authors proved this with the additional square-free hypothesis on the solutions. It is also proved that finite square-free non-degenerate involutive set-theoretic solutions associated to a left brace are multipermutation solutions.