Skew left braces and 2-reductive solutions of the Yang-Baxter equation

Autor:	Jedlička, Přemysl, Pilitowska, Agata
Rok vydání:	2023
Předmět:	Mathematics - Combinatorics Mathematics - Rings and Algebras Primary: 16T25 Secondary: 20B25
Druh dokumentu:	Working Paper
Popis:	We study 2-reductive non-involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation. We give a combinatorial construction of any such solution of any (even infinite) size. We also prove that solutions associated to a skew left brace are 2-reductive if and only if the skew left brace is nilpotent of class 2. Moreover, all such skew left braces are actually bi-skew left braces. We focus on these structures and we give several equivalent properties characterizing solutions associated to bi-skew left braces. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.15154 Zobrazit plný text záznamu View this record from Arxiv