Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
E. Acri , Rafał Lutowski , L. Vendramin
AbstractUsing Bieberbach groups, we study multipermutation involutive solutions to the Yang–Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups. An algorithm to find subgroups of a Bieberbach group isomorphic to the Promislow subgroup is introduced and then used in the case of structure group of involutive solutions. To extend the results related to retractability to non-involutive solutions, following the ideas of Meng, Ballester-Bolinches and Romero, we develop the theory of right p-nilpotent skew braces. The theory of left p-nilpotent skew braces is also developed and used to give a short proof of a theorem of Smoktunowicz in the context of skew braces.
|Journal series||International Journal of Algebra and Computation, ISSN 0218-1967, e-ISSN 1793-6500, (N/A 70 pkt)|
|Publication size in sheets||0.3|
|Keywords in English||Bieberbach group, Yang-Baxter equation, set-theoretic solution, multipermutation solution, unique product property, skew brace|
|Score||= 70.0, 18-02-2020, ArticleFromJournal|
|Publication indicators||: 2018 = 0.89; : 2018 = 0.419 (2) - 2018=0.536 (5)|
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.