Iterated matched products of finite braces and simplicity; new solutions of the Yang-Baxter equation
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- by D. Bachiller, F. Cedó, E. Jespers and J. Okniński PDF
- Trans. Amer. Math. Soc. 370 (2018), 4881-4907 Request permission
Abstract:
Braces were introduced by Rump as a promising tool in the study of the set-theoretic solutions of the Yang-Baxter equation. It has been recently proved that, given a left brace $B$, one can construct explicitly all the non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation such that the associated permutation group is isomorphic, as a left brace, to $B$. It is hence of fundamental importance to describe all simple objects in the class of finite left braces. In this paper we focus on the matched product decompositions of an arbitrary finite left brace. This is used to construct new families of finite simple left braces.References
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Additional Information
- D. Bachiller
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
- Email: dbachiller@mat.uab.cat
- F. Cedó
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
- Email: cedo@mat.uab.cat
- E. Jespers
- Affiliation: Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium
- MR Author ID: 94560
- Email: eric.jespers@vub.be
- J. Okniński
- Affiliation: Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland
- Email: okninski@mimuw.edu.pl
- Received by editor(s): October 3, 2016
- Published electronically: February 1, 2018
- Additional Notes: The first and second authors were partially supported by grants MINECO-FEDER MTM2014-53644-P and MTM2017-83487-P (Spain)
The third author was supported in part by Onderzoeksraad of Vrije Universiteit Brussel and Fonds voor Wetenschappelijk Onderzoek (Belgium)
The fourth author was supported by National Science Centre grants 2013/09/B/ST1/04408 and 2016/23/B/ST1/01045 (Poland) - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 4881-4907
- MSC (2010): Primary 16T25, 20E22, 20F16
- DOI: https://doi.org/10.1090/tran/7180
- MathSciNet review: 3812099