Drinfeld formulated the set-theoretic Yang Baxter equation (YBE) in an attempt to simplify the classification problem for solutions of the quantum YBE from physics. In the intervening 35 years, investigations of the set-theoretic YBE have called upon a wide array of algebraic structures: groups, quasigroups, racks, quandles, cycle sets, and (skew)-braces, just to name a few. In this talk, we will discuss how Bruck loops and Moufang loops are central to understanding a class of solutions that exhibit a ``dihedral" symmetry. This is joint work with Anna Zamojska-Dzienio.
Dihedral solutions of the set theoretic Yang-Baxter equation
Dihedral solutions of the set theoretic Yang-Baxter equation