Geometrization of trigonometric solutions of the associative and classical Yang-Baxter equations

Abstract

We describe a geometric construction of all nondegenerate trigonometric solutions of the associative and classical Yang-Baxter equations. In the associative case the solutions come from symmetric spherical orders over the irreducible nodal curve of arithmetic genus $1$, while in the Lie case they come from spherical sheaves of Lie algebras over the same curve.