Braces, radical rings, and the quantum Yang-Baxter equation

JOURNAL OF ALGEBRA

卷:307

Article

Rump, Wolfgang

关键词: quantum Yang-Baxter equation;    set-theoretical solution;    radical ring;    cycle set;    brace;    square-free;   

DOI  :  10.1016/j.jalgebra.2006.03.040

来源: Elsevier

【 摘 要 】

Non-degenerate cycle sets are equivalent to non-degenerate unitary set-theoretical solutions of the quantum Yang-Baxter equation. We embed such cycle sets into generalized radical rings (braces) and study their interaction in this context. We establish a Galois theory between ideals of braces and quotient cycle sets. Our main result determines the relationship between two square-free cycle sets operating transitively on each other. (C) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free