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

Anastasia Doikou, Alexandros Ghionis, Bart Vlaar

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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 generalise recent relevant results on set theoretic solutions and their q-deformed analogues.
Original languageEnglish
Article number78
JournalLetters in Mathematical Physics
Publication statusPublished - 8 Aug 2022


  • math.QA
  • math-ph
  • math.MP

ASJC Scopus subject areas

  • Mathematics(all)


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