Central elements of the elliptic Yang--Baxter algebra at roots of unity

TL;DR

This paper identifies central elements of the elliptic Yang-Baxter algebra associated with the eight-vertex model when the crossing parameter is a rational multiple of its periods, advancing understanding of algebraic structures at roots of unity.

Contribution

It provides explicit central elements of the elliptic Yang-Baxter algebra at roots of unity, a novel result in the study of integrable models.

Findings

Explicit construction of central elements at roots of unity

Enhanced understanding of algebraic structure at special parameter values

Potential applications to solvable models and quantum groups

Abstract

We give central elements of the Yang-Baxter algebra for the $R$-matrix of the eight-vertex model, in the case when the crossing parameter is a rational multiple of one of the periods.