Constructions of BiHom-X algebras and bimodules of some BiHom-dialgebras

I. Laraiedh, S. Silvestrov


The aim of this paper is to introduce and to develop several methods for constructions of BiHom-X algebras by extending composition methods, and by using Rota-Baxter operators and some elements of centroids. The bimodules of BiHom-left symmetric dialgebras, BiHom-associative dialgebras and BiHom-tridendriform algebra are defined, and it is shown that a sequence of this kind of bimodules can be constructed. Their matched pairs of BiHom-left symmetric, BiHom-associative dialgebras BiHom-tridendriform algebra are introduced and methods for their constructions and properties are investigated.


BiHom-X algebra, BiHom-left-symmetric dialgebra, matched pair, bimodule, centroid

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