Andrew Hardt: Groupoids and the Yang–Baxter Equation

Speaker
Andrew Hardt, University of Illinois Urbana-Champaign

Abstract
It was known at least as far back as Baxter that solutions to the Yang–Baxter equation in the field-free six-vertex and eight-vertex models carry natural composition laws making solution sets into disjoint unions of groups. For the general (non-field-free) six-vertex model, Bump and Naprienko showed that the appropriate structure is a groupoid rather than a group. In joint work in progress with Daniel Bump and Travis Scrimshaw, we show that the six-vertex groupoid can be realized as an action groupoid, and establish a groupoid structure on the semi-field-free eight-vertex model (\(a_1=a_2,b_1=b_2\)).