In this paper, we first propose the concepts of BiHom-Ω-associative algebras, BiHom-Ω-dendriform algebras, BiHom-Ω-pre-Lie algebras and BiHom-Ω-Lie algebras. We then obtain a new BiHom-Ω-associative (resp. Lie) algebra by defining a new multiplication on a BiHom-Ω-associative (resp. Lie) algebra with the Rota-Baxter family of weight λ.In addition, we generalize the classical relationships of associative algebras, pre-Lie algebras, dendriform algebras and Lie algebras to the BiHom-Ω version.
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Liu et al. (2024) studied this question.
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