Solutions of Yang–Baxter Equation of Mock-Lie Algebras and Related Rota Baxter Algebras

Abstract

This paper discusses the relationship between Mock-Lie algebras, Lie algebras, and Jordan algebras. It highlights the importance of the Yang–Baxter equation and symplectic forms in the study of integrable systems, quantum groups, and topological quantum field theory. The paper also proposes studying the admissible associative Yang–Baxter equation in algebras and characterizing Q-Admissible Solutions of the Associative Yang–Baxter Equation in Rota–Baxter Algebras. Finally, it discusses the interplay of coalgebra, r-matrix, and pseudo-Euclidean forms in the context of Jordan algebras and its applications in quantum groups and integrable systems.

Keywords

• Yang–Baxter equation
• Mock-Lie algebras
• Rota–Baxter algebra
• Lie structure