杨-巴克斯特方程不可分解对合集合论解复盖中的素数

IF 0.4 4区数学 Q4 MATHEMATICS Bulletin of the Belgian Mathematical Society-Simon Stevin Pub Date : 2023-09-30 DOI:10.36045/j.bbms.230429

Wolfgang Rump

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引用次数: 0

摘要

Jan Okniński提出了这样一个问题:划分Yang-Baxter方程有限不可分解集合论解的大小$n$的素数是否与划分相关置换群的顺序有关。他用Cedó证明了如果$n$是无平方的，两个素数集相等。我们刻画了等式，并证明了解的满射态射允许正则分解为一个覆盖和一个由双理想给出的态射。将素数集不相等解的存在性简化为不可伸缩解。证明了不相等是可能的，并构造了一个极小的例子。

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Primes in coverings of indecomposable involutive set-theoretic solutions to the Yang-Baxter equation

Jan Okniński raised the question whether the primes dividing the size $n$ of a finite indecomposable set-theoretic solution to the Yang-Baxter equation are related to the primes dividing the order of the associated permutation group. With Cedó he proved that both prime sets are equal if $n$ is square-free. We characterize equality and prove that surjective morphisms of solutions admit a canonical factorization into a covering and a morphism given by a brace ideal. The existence of solutions with non-equality of the prime sets is reduced to irretractable solutions. It is proved that non-equality is possible, and a minimal example is constructed..

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来源期刊

Bulletin of the Belgian Mathematical Society-Simon Stevin 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Bulletin of the Belgian Mathematical Society - Simon Stevin (BBMS) is a peer-reviewed journal devoted to recent developments in all areas in pure and applied mathematics. It is published as one yearly volume, containing five issues. The main focus lies on high level original research papers. They should aim to a broader mathematical audience in the sense that a well-written introduction is attractive to mathematicians outside the circle of experts in the subject, bringing motivation, background information, history and philosophy. The content has to be substantial enough: short one-small-result papers will not be taken into account in general, unless there are some particular arguments motivating publication, like an original point of view, a new short proof of a famous result etc. The BBMS also publishes expository papers that bring the state of the art of a current mainstream topic in mathematics. Here it is even more important that at leat a substantial part of the paper is accessible to a broader audience of mathematicians. The BBMS publishes papers in English, Dutch, French and German. All papers should have an abstract in English.