Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation

Anastasia Doikou, Alexandros Ghionis, Bart Vlaar

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1 Citation (Scopus)
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Abstract

We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang–Baxter equation and their q-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld twists, we show that the quantum algebras produced from set-theoretic solutions and their q-analogues are in fact quasi-triangular quasi-bialgebras. Specific illustrative examples compatible with our generic findings are worked out. In the q-deformed case of set-theoretic solutions, we also construct admissible Drinfeld twists similar to the set-theoretic ones, subject to certain extra constraints dictated by the q-deformation. These findings greatly generalize recent relevant results on set-theoretic solutions and their q-deformed analogues.

Original languageEnglish
Article number78
JournalLetters in Mathematical Physics
Volume112
Issue number4
DOIs
Publication statusPublished - 8 Aug 2022

Keywords

  • Drinfeld twists
  • Quasi-bialgebras
  • Set-theoretic Yang-Baxter equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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