BiHom-$\Omega$-associative algebras and related structures

Abstract

In this paper, we first propose the concepts of BiHom-$\Omega$-associative algebras, BiHom-$\Omega$-dendriform algebras, BiHom-$\Omega$-pre-Lie algebras and BiHom-$\Omega$-Lie algebras. We then obtain a new BiHom-$\Omega$-associative (resp. Lie) algebra by defining a new multiplication on a BiHom-$\Omega$-associative (resp. Lie) algebra with the Rota-Baxter family of weight $\lambda$.In addition, we generalize the classical relationships of associative algebras, pre-Lie algebras, dendriform algebras and Lie algebras to the BiHom-$\Omega$ version.