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Automorphisms of algebraic varieties and Yang-Baxter equations. (English) Zbl 0609.14028
A family of algebraic equations arising from exactly solvable models in statistical mechanics are the so-called Yang-Baxter equations. All the known solutions of these equations are parametrized by rational or elliptic functions. The author observes that the algebraic varieties parametrizing the exactly solvable models are endowed with a group of automorphisms which, in general, due to statistical mechanical reasons, must be infinite. Then such varieties cannot be of general type and in dimension 1 this makes clear the occurrence of curves of genus 0 and 1.
Reviewer: C.Turrini
MSC:
14L30Group actions on varieties or schemes (quotients)
35Q99PDE of mathematical physics and other areas
82B05Classical equilibrium statistical mechanics (general)