Yang-Baxter systems, solutions and applications

TL;DR

This paper explores Yang-Baxter systems, presenting examples and solutions for constant and spectral-dependent types, and discusses their applications in physics, especially in quantum integrable models and Hopf algebras.

Contribution

It provides a comprehensive overview of Yang-Baxter systems, including known solutions and strategies for solving related systems, advancing understanding in mathematical physics.

Findings

Complete solution for constant systems in dimension two

Examples of both constant and spectral-dependent systems

Proposed strategy for solving systems related to quantum doubles

Abstract

Two types of Yang-Baxter systems play roles in the theoretical physics -- constant and colour dependent. The constant systems are used mainly for construction of special Hopf algebra while the colour or spectral dependent for construction of quantum integrable models. Examples of both types together with their particular solutions are presented. The complete solution is known only for the constant system related to the quantized braided groups in the dimension two. The strategy for solution of the system related to quantum doubles is suggested and partial results are presented.