Abelian maps, brace blocks, and solutions to the Yang-Baxter equation

被引：7
|
作者：
Koch, Alan [1 ]
机构：
[1] Agnes Scott Coll, Dept Math, 141 E Coll Ave, Decatur, GA 30030 USA
来源：
JOURNAL OF PURE AND APPLIED ALGEBRA | 2022年 / 226卷 / 09期
关键词：
Yang-Baxter equation; Skew left braces; Bi-skew braces; Abelian maps; POINT FREE ENDOMORPHISMS; SET-THEORETIC SOLUTIONS;
D O I：
10.1016/j.jpaa.2022.107047
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a finite nonabelian group. We show how an endomorphism of G with abelian image gives rise to a family of binary operations {o(n) : n is an element of Z(>= 0)} on G such that (G, o(m), o(n)) is a skew left brace for all m, n >= 0. A brace block gives rise to a number of non-degenerate set-theoretic solutions to the Yang-Baxter equation. We give examples showing that the number of solutions obtained can be arbitrarily large.(c) 2022 Elsevier B.V. All rights reserved.
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页数：15
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