27 citations · 63 across the 6 of their papers we have counts for
6 papers
A Poincaré-Birkhoff-Witt theorem for the universal enveloping algebra of a Rota-Baxter Lie algebra
Zhi-Cheng Zhu, Xing Gao, Li Guo +1
Rota-Baxter associative algebras and Rota-Baxter Lie algebras are both important in mathematics and mathematical physics, with the former a basic structure in quantum field renorma…
Representations of Polynomial Rota-Baxter Algebras
Li Qiao, Jun Pei
A Rota--Baxter operator is an algebraic abstraction of integration, which is the typical example of a weight zero Rota-Baxter operator. We show that studying the modules over the p…
Averaging algebras, Schröder numbers, rooted trees and operads
Li Guo, Jun Pei
In this paper, we study averaging operators from an algebraic and combinatorial point of view. We first construct free averaging algebras in terms of a class of bracketed words cal…
Rota-Baxter operators on and solutions of the classical Yang-Baxter equation
Jun Pei, Chengming Bai, Li Guo
We explicitly determine all Rota-Baxter operators (of weight zero) on under the Cartan-Weyl basis. For the skew-symmetric operators, we give the corresponding skew-symmet…
Splitting of operads and Rota-Baxter operators on operads
Jun Pei, Chengming Bai, Li Guo
This paper establishes a uniform procedure to split the operations in any algebraic operad, generalizing previous known notions of splitting algebraic structures from the dendrifor…
Replicating of binary operads, Koszul duality, Manin products and average operators
Jun Pei, Chengming Bai, Li Guo +1
We consider the notions of the replicators, including the duplicator and triplicator, of a binary operad. As in the closely related notions of di-Var-algebra and tri-Var-algebra in…