Yang-Baxter Equation on Two-Dimensional Lattice and Some Infinite Dimensional Algebras

TL;DR

This paper demonstrates that the Yang-Baxter equation is equivalent to algebra associativity on 2D lattices and constructs related infinite-dimensional algebras, including FFZ and quantum sl(2), from link operators.

Contribution

It establishes a novel connection between the Yang-Baxter equation and algebra associativity, and derives new algebraic structures from link operators on lattices.

Findings

Yang-Baxter equation is equivalent to algebra associativity

Construction of FFZ algebras from link operators

Derivation of quantum sl(2) algebra from FFZ generators

Abstract

We show that the Yang-Baxter equation is equivalent to the associativity of the algebra generated by non-commuting link operators. Starting from these link operators we build out the (FFZ) algebras, the $s\ell_q (2)$ is derived by considering a special combination of the generators of (FFZ) algebra.