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Some generalized Hom-algebra structures. (English) Zbl 1394.17001

Summary: In this paper, we introduce generalized left-Hom-symmetric algebras and generalized Hom-dendriform algebras as well as the corresponding modules. We investigate the connection between these categories of generalized Hom-algebras and -modules. We give various constructions of these generalized Hom-algebra structures from either a given one or an ordinary one. We prove that any generalized Hom-dialgebras give rise to generalized Hom-Leibniz-Poisson algebras and generalized Hom-Poisson dialgebras.

MSC:

17A30 Nonassociative algebras satisfying other identities
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Full Text: Euclid