Automorphisms of algebraic varieties and Yang–Baxter equations

Abstract

It is shown that commuting transfer matrix models in statistical mechanics are parametrized by algebraic varieties having a set of automorphisms deduced from the so-called ‘‘inversion relation.’’ In general this set of automorphisms is infinite: this shows that for algebraic varieties of dimension 1, the models are parametrized by algebraic curves of genus 0 or 1.