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arXiv 2407.07907math.QA
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基数为$p^n$的Yang-Baxter方程的单解

Simple solutions of the Yang-Baxter equation of cardinality $p^n$

Ferran Cedo, Jan Okninski

备注：
arXiv admin note: text overlap with arXiv:2401.12904, arXiv:2212.06753, arXiv:2112.07271, arXiv:2012.08400
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AI总结：

该研究构造了两类Yang-Baxter方程的集合论解，同时肯定回答了Castelli提出的相关存在性问题。

摘要：

对每个素数p和整数$n>1$，构造了基数$|X|=p^n$的Yang-Baxter方程的一个单的、对合的、非退化的集合论解$(X,r)$。此外，对每个不是素数平方的非无平方因子正整数m，构造了基数$|X|=m$的Yang-Baxter方程的一个非单的、不可分解的、不可收缩的、对合的、非退化的集合论解$(X,r)$。本文还肯定地回答了Castelli最近提出的关于某类奇异解存在性的问题。

英文摘要：

For every prime number p and integer $n>1$, a simple, involutive, non-degenerate set-theoretic solution $(X,r$) of the Yang-Baxter equation of cardinality $|X| = p^n$ is constructed. Furthermore, for every non-(square-free) positive integer m which is not the square of a prime number, a non-simple, indecomposable, irretractable, involutive, non-degenerate set-theoretic solution $(X,r)$ of the Yang-Baxter equation of cardinality $|X| = m$ is constructed. A recent question of Castelli on the existence of singular solutions of certain type is also answered affirmatively.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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