Rota–Baxter algebras and dendriform algebras

By Kurusch Ebrahimi-Fard, Li Guo. 2005

172 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/794f4e21cbb95add83113009af08806692510ac3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Deformations of associative Rota-Baxter operators (2019, background): “RotaBaxter operators also give rise to dendriform structures introduced by Loday [24] (see also [14]).”
Rota–Baxter Hom-Lie–Admissible Algebras (2011, background): “Rota–Baxter algebras are related to dendriform algebras via a pair of adjoint functors [24, 26].”
Grobner-Shirshov Bases for Associative Algebras with Multiple Operators and Free Rota-Baxter Algebras ∗† (2008, methodology): “K. Ebrahimi-Fard and L. Guo [ 29 ] further constructed the free associative Rota-Baxter algebras by using the Rota-Baxter words.”
On Differential Rota-Baxter Algebras (2007, methodology): “In the last few years, major progresses have been made in both differential algebra and Rota-Baxter algebra, with applications in broad areas in mathematics and physics [1, 2, 5, 8, 12 , 13, 15, 16, 18, 28, 29].”
Embedding of dendriform algebras into Rota-Baxter algebras (2011, background): “ota—Baxter algebras of arbitrary weight and obtained 1 2 V. YU. GUBAREV1), P.S. KOLESNIKOV2) as result both dendriform dialgebra and dendriform trialgebra. In the paper by K. Ebrahimi-Fard and L. Guo [17] in 2007, universal enveloping Rota—Baxter algebras of weight λ for dendriform dialgebras and tr”