RotaBaxter Algebras and Dendriform Algebras
Abstract
In this paper we study the adjoint functors between the category of RotaBaxter algebras and the categories of dendriform dialgebras and trialgebras. In analogy to the wellknown theory of the adjoint functor between the category of associative algebras and Lie algebras, we first give an explicit construction of free RotaBaxter algebras and then apply it to obtain universal enveloping RotaBaxter 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 RotaBaxter algebras.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2005
 arXiv:
 arXiv:math/0503647
 Bibcode:
 2005math......3647E
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Combinatorics;
 16A06;
 47B99
 EPrint:
 Typos corrected and the last section on analog of PoincareBirkhoffWitt theorem deleted for a gap in the proof