Solutions of the Yang-Baxter equation associated with a left brace

2015/03/10 by David Bachiller, Bachiller, David, Ferran Cedo +3 · 1 citation
Mathematics · #16T25 (Primary) #20B30 #81R50 (Secondary) #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA) #math.GR #math.QA #msc:16T25 #msc:20B30 #msc:81R50

paper · pdf · doi:10.48550/arxiv.1503.02814

18 pages

arxiv created 2015/03/10 · arxiv updated 2015/03/11

Abstract

Given a left brace G, a method to construct all the involutive, non-degenerate set-theoretic solutions (Y,s) of the YBE, such that G(Y,s)≅ G is given. This method depends entirely on the brace structure of G.

Cited by

• Finite groups in which every proper characteristic subgroup is cyclic

Related

• Solutions of the Yang-Baxter equation associated to skew left braces, with applications to racks
• New simple solutions of the Yang-Baxter equation and solutions associated to simple left braces
• A characterization of finite simple set-theoretic solutions of the Yang-Baxter equation
• Braces and the Yang-Baxter equation
• Left semi-braces and solutions to the Yang-Baxter equation