Tue, 31 Mar 2026, 1:25 pm MDT
Drinfeld formulated the set-theoretic Yang Baxter equation (YBE), $(r\times 1_Q)(1_Q\times r)(r\times 1_Q)=(1_Q\times r)(r\times 1_Q)(1_Q\times r)$ for a map $r:Q^2\to Q^2$, 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 $r$ that exhibit a ``dihedral" symmetry: $(\tau r)^2=1_{Q^2}$, where $\tau(x, y)=(y, x)$. This is joint work with Anna Zamojska-Dzienio.
[preprint]