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arXiv · 2203.03400

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

Anastasia Doikou·Alexandros Ghionis·Bart Vlaar
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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 generalise recent relevant results on set theoretic solutions and their q-deformed analogues.

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BibTeXRIS

Anastasia Doikou, Alexandros Ghionis, Bart Vlaar. 2022-03-07. Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation. https://doi.org/10.1007/s11005-022-01572-9

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