Yang–Baxter Equations, Computational Methods and Applications

Abstract

Computational methods are an important tool for solving the Yang–Baxter equations (in small dimensions), for classifying (unifying) structures and for solving related problems. This paper is an account of some of the latest developments on the Yang–Baxter equation, its set-theoretical version and its applications. We construct new set-theoretical solutions for the Yang–Baxter equation. Unification theories and other results are proposed or proven.

Keywords

• Yang–Baxter equation
• computational methods
• universal gate
• non-associative structures
• associative algebras
• Jordan algebras
• Lie algebras