Counterexample to a conjecture about braces

被引：73

作者：

Bachiller, David ^{[1
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Barcelona, Spain

来源：

JOURNAL OF ALGEBRA | 2016年 / 453卷

关键词：

Braces; IYB group; Bijective; 1-cocycle; Radical rings; Hopf-Galois extensions; Nilpotent group; Lie algebras; LSA structures; YANG-BAXTER EQUATION; FIELD-EXTENSIONS;

D O I：

10.1016/j.jalgebra.2016.01.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find an example of a finite solvable group (in fact, a finite p-group) in which is not possible to define a left brace structure or, equivalently, which is not an IYB group. This answers a question posed by Cedo, Jespers and del Rio related to the Yang-Baxter equation. Our argument is an improvement of an argument of Rump, using results about Hopf-Galois extensions and LSA structures. We explain explicitly the relation between these two areas of mathematics and brace theory, hoping that it will be useful in the future. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：160 / 176

页数：17

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