LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS

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Konuralp Journal of Mathematics
Volume:3 Issue:2
LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS

LEFT-HOM-SYMMETRIC AND HOM-POISSON DIALGEBRAS

Authors : Bakayoko I, Bangoura M

Pages : 42-53

View : 15 | Download : 13

Publication Date : 2015-10-01

Article Type : Research Paper

Abstract :The aim of this paper is to introduce left-Hom-symmetric dial- gebras insert ignore into journalissuearticles values(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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