Set-theoretic Yang-Baxter equation, braces and drinfeld twists

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Abstract

We consider involutive, non-degenerate, finite set-theoretic solutions of the Yang-Baxter equation (YBE). Such solutions can be always obtained using certain algebraic structures that generalize nilpotent rings called braces. Our main aimhere is to express such solutions in terms of admissible Drinfeld twists substantially extending recent preliminary results. We first identify the generic form of the twists associated to set-theoretic solutions and we show that these twists are admissible, i.e. they satisfy a certain co-cycle condition. These findings are also valid for Baxterized solutions of the YBE constructed from the set-theoretical ones.

Original languageEnglish
Article number415201
JournalJournal of Physics A: Mathematical and Theoretical
Volume54
Issue number41
Early online date26 Aug 2021
DOIs
Publication statusPublished - 15 Oct 2021

Keywords

  • Braces
  • Drinfeld twists
  • Quantum groups
  • Yang-Baxter equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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