Hopf algebras in SupLat and set-theoretical YBE solutions

Abstract: Skew braces have recently attracted attention as a method to study set-theoretical solutions of the Yang-Baxter equation. In this talk, we will present a new approach for studying these solutions, by looking at Hopf algebras in the category of complete lattices and join-preserving morphisms, denoted by SupLat. Any Hopf algebra, H in SupLat, has a corresponding group, R(H), which we call its remnant and a co-quasitriangular structure on H induces a brading operator on R(H), which induces a skew brace structure on R(H). From this correspondence, we will recover several aspects of the theory of skew braces. In particular, we will construct the universal skew brace of a set-theoretical YBE solution, as the remnant of an FRT-type reconstruction in SupLat.

quantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This online seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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