斜左括号的Jordan-Hölder定理及其在Yang-Baxter方程多置换解中的应用

IF 1.3 3区数学 Q1 MATHEMATICS Proceedings of the Royal Society of Edinburgh Section A-Mathematics Pub Date : 2023-04-24 DOI:10.1017/prm.2023.37

A. Ballester-Bolinches, R. Esteban-Romero, V. Pérez-Calabuig

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引用次数: 2

摘要

斜左括号是在研究Yang-Baxter方程的非退化集论解时自然产生的。为了理解斜左括号的代数结构，对其分解为最小子结构的研究是相关的。引入了主要级数，并证明了有限斜左括号Jordan-Hölder定理的一个强化形式。给出了右零幂的一个性质及其在多置换解中的应用。

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A Jordan–Hölder theorem for skew left braces and their applications to multipermutation solutions of the Yang–Baxter equation

Skew left braces arise naturally from the study of non-degenerate set-theoretic solutions of the Yang–Baxter equation. To understand the algebraic structure of skew left braces, a study of the decomposition into minimal substructures is relevant. We introduce chief series and prove a strengthened form of the Jordan–Hölder theorem for finite skew left braces. A characterization of right nilpotency and an application to multipermutation solutions are also given.

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来源期刊

Proceedings of the Royal Society of Edinburgh Section A-Mathematics 数学-数学

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.