Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces

E. Acri , Rafał Lutowski , L. Vendramin

Abstract

Using 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.
Author E. Acri
E. Acri,,
-
, Rafał Lutowski (FMPI/IM)
Rafał Lutowski,,
- Institute of Mathematics
, L. Vendramin
L. Vendramin,,
-
Journal seriesInternational Journal of Algebra and Computation, ISSN 0218-1967, e-ISSN 1793-6500, (N/A 70 pkt)
Issue year2020
Vol30
No1
Pages91-115
Publication size in sheets0.30
Keywords in EnglishBieberbach group, Yang-Baxter equation, set-theoretic solution, multipermutation solution, unique product property, skew brace
ASJC Classification2600 General Mathematics
DOIDOI:10.1142/S0218196719500656
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 28-05-2020, ArticleFromJournal
Publication indicators WoS Citations = 0.000; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.890; WoS Impact Factor: 2018 = 0.419 (2) - 2018=0.536 (5)
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