Rota-Baxter Algebras and Dendriform Algebras

Details Rota-Baxter Algebras and Dendriform Algebras Rota-Baxter Algebras and Dendriform Algebras

2005-03-28

arxiv.org/abs/math/0503647v3

Journal of Pure and Applied Algebra, Vol 212, Issue 2, 2008, 320-339.

Mathematics

Rings and Algebras

Typos corrected and the last section on analog of Poincare-Birkhoff-Witt theorem deleted for a gap in the proof

Scientific paper

10.1016/j.jpaa.2007.05.025

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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