Hom-O-Operators and Hom-Yang-Baxter Equations

الملخص EN

In Hom-Lie set, we introduce the concept of Hom-O-operators and study its relation with classical Hom-Yang-Baxter equation, as well as left-symmetric Hom-algebras.

We construct the corresponding relation between left-symmetric Hom-algebras and Hom-1-cocycles, which are both related to classical Hom-Yang-Baxter equation.

Moreover, in Hom-algebra setting, we establish the equivalent relationship between AHYBE (associative Hom-Yang-Baxter equations) and O-operators on Frobenius monoidal Hom-algebras.