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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

advances in mathematical physics

Hom-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi mathvariant="script">O</mml:mi></mml:mrow></mml:math>-Operators and Hom-Yang-Baxter Equations

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