Article ID Journal Published Year Pages File Type
4598123 Journal of Pure and Applied Algebra 2008 20 Pages PDF
Abstract

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.

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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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