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Bimodules and Rota-Baxter Relations

Ibrahima Bakayoko and Momo Banagoura

In this paper we introduce and study Hom-type bimodules of some Hom-algebraic structures endowed with Rota-Baxter relations. We introduce bimodules over Homassociative Rota-Baxter algebras and give their various twisting and their connection with bimodules over Hom-preLie algebras. Then we introduce Rota-Baxter q- Homtridendriform algebras. Next we express axioms defining q-Hom-tridendriform algebras by mean of vector basis. Moreover we introduce bimodules over q-Homtridendriform algebras and give some examples, and prove that they are closed by twisting. Finally we give their connection with Hom-associative Rota-Baxter bimodules.