BiHom--associative algebras and related structures

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