alexa DENDRIFORM ALGEBRAS AND ROTA-BAXTER OPERATORS REVISITED IN SEVERAL DIRECTIONS
Mathematics

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Raul Felipe

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The main purpose of this article is to move the study of dendriform algebras and Rota-Baxter operators to a nonassociative setting beyondthe Lie algebras. We show how to associate structures of dendriform type to alternative and exible algebras and characterize the Rota-Baxter op-erators corresponding to them, in order to extend some results that haveappeared in the literature for the associative case. These objects are stud-ied in some detail. Also, we show that the usual version of Rota-Baxter operators acts on Leibniz algebras in the same form that they act on Lie algebras and in particular can be used into Leibniz-admissible algebras.As a consequence we arrive to the notion of admissible dendriform al-gebra. Additionally, we propose the concept of generalized dendriform algebra and describe a connection of it with the left-symmetric dialgebras recently introduced by the author.

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This article was published in ComunicaciĆ³n del CIMAT and referenced in Journal of Generalized Lie Theory and Applications

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