Counterexample to a conjecture about braces

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• 作者：David Bachiller ^{dbachiller@mat.uab.cat" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 16N20 ; 20D15 ; 81R50 ; secondary ; 16T25 ; 12F10 ; 17B30 ; 17B60
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：453
• 期：Complete
• 页码：160-176
• 全文大小：378 K

文摘

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 Cedó, Jespers and del Río 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.