alexa Rota–Baxter algebras and dendriform algebras
Mathematics

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Kurusch EbrahimiFard, Li Guo

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In this paper we study the adjoint functors between the category of Rota–Baxter algebras and the categories of dendriform dialgebras and trialgebras. In analogy to the well-known theory of the adjoint functor between the category of associative algebras and Lie algebras, we first give an explicit construction of free Rota–Baxter algebras and then apply it to obtain universal enveloping Rota–Baxter algebras of dendriform dialgebras and trialgebras. We further show that free dendriform dialgebras and trialgebras, as represented by binary planar trees and planar trees, are canonical subalgebras of free Rota–Baxter algebras.

This article was published in Journal of Pure and Applied Algebra and referenced in Journal of Generalized Lie Theory and Applications

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