LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS

Authors : Bakayoko I., Bangoura M.
Pages : 42-53
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Publication Date : 2015-10-01
Article Type : Research
Abstract :The aim of this paper is to introduce left-Hom-symmetric dial- gebras (which contain left-Hom-symmetric algebras or Hom-preLie algebras and Hom-dialgebras as special cases) and Hom-Poisson dialgebras. We give some examples and some construction theorems by using the composition con- struction. We prove that the commutator bracket of any left-Hom-symmetric dialgebra provides Hom-Leibniz algebra. We also prove that bimodules over Hom-dialgebras are closed under twisting. Next, we show that bimodules over Hom-dendriform algebras D extend to bimodules over the left-Hom-symmetric algebra associated to D. Finally, we give some examples of Hom-Poisson dial- gebras and prove that the commutator bracket of any Hom-dialgebra structure map leads to Hom-Poisson dialgebra.
Keywords : Hom-Leibniz algebras, left-Hom-symmetric dialgebras, left-Hom- symmetric algebras, Hom-dendriform algebras

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