12 citations · 54 across the 18 of their papers we have counts for
18 papers
Bialgebra theory, the Yang-Baxter equation and relative Rota-Baxter operators for diassociative algebras
Hui Hu, Yizhen Li, Guilai Liu +1
In this paper, we develop a bialgebra theory for diassociative algebras. Inspired by the notion of a quadratic diassociative algebra, we introduce the concept of a Manin triple of…
Para-differential Rota-Baxter algebras and their free objects by Gröbner-Shirshov bases
Li Guo, Aniruddha Talele, Shilong Zhang +1
The algebraic formulation of the derivation and integration related by the First Fundamental Theorem of Calculus (FFTC) gives rise to the notion of differential Rota-Baxter algebra…
Noncommutative Novikov bialgebras and differential antisymmetric infinitesimal bialgebras with weight
Shanghua Zheng, Yizhen Li, Liushuting Yang +1
This paper first develops a bialgebra theory for a noncommutative Novikov algebra, called a noncommutative Novikov bialgebra, which is further characterized by matched pairs and Ma…
Extended (tri)dendriform algebras, pre-Lie algebras and post-Lie algebras as companion structures of extended Rota-Baxter algebras
Shanghua Zheng, Shiyu Huang, Li Guo
Under the common theme of splitting of operations, the notions of (tri)dendriform algebras, pre-Lie algebras and post-Lie algebras have attracted sustained attention with broad app…
Extended Rota-Baxter algebras, diagonally colored Delannoy paths and Hopf algebras
Shanghua Zheng, Li Guo, Huizhen Qiu
The Rota-Baxter operator and the modified Rota-Baxter operator on various algebras are both important in mathematics and mathematical physics. The former is originated from the int…
Construction of free quasi-idempotent differential Rota-Baxter algebras by Gröbner-Shirshov bases
Huizhen Qiu, Shanghua Zheng, Yangfan Dan
Differential operators and integral operators are linked together by the first fundamental theorem of calculus. Based on this principle, the notion of a differential Rota-Baxter al…
Interlacing, integrals of Hurwitz series and differential equations
Shanghua Zheng
In this paper, we first introduce the unlacing of Hurwitz series, which can be viewed as an inverse of interlacing, and develop the basic properties of unlacing, interlacing and in…
-TD algebras, generalized shuffle products and left counital Hopf algebras
Hengyi Luo, Shanghua Zheng
The theory of operated algebras has played a pivotal role in mathematics and physics. In this paper, we introduce a -TD algebra that appropriately includes both the Rota-Baxter…
Quivers and path semigroups characterized by locality conditions
Li Guo, Shanghua Zheng
The notion of locality semigroups was recently introduced with motivation from locality in convex geometry and quantum field theory. We show that there is a natural correspondence…
Several locality semigroups, path semigroups and partial semigroups
Shanghua Zheng
Locality semigroups were proposed recently as one of the basic locality algebraic structures, which are studied in mathematics and physics. Path semigroups and partial semigroups w…
Left counital Hopf algebra structures on free commutative Nijenhuis algebras
Shanghua Zheng, Li Guo
Motivated by the Hopf algebra structures established on free commutative Rota-Baxter algebras, we explore Hopf algebra related structures on free commutative Nijenhuis algebras. Ap…
Universal enveloping algebras and Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras
Li Guo, Bin Zhang, Shanghua Zheng
A Hom-type algebra is called involutive if its Hom map is multiplicative and involutive. In this paper, we obtain an explicit construction of the free involutive Hom-associative al…
Rota-Baxter type operators, rewriting systems and Gröbner-Shirshov bases
Xing Gao, Li Guo, William Y. Sit +1
In this paper we apply the methods of rewriting systems and Gröbner-Shirshov bases to give a unified approach to a class of linear operators on associative algebras. These operator…
Free involutive Hom-semigroups and Hom-associative algebras
Li Guo, Shanghua Zheng
In this paper we construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence,…
Rota-Baxter operators on the polynomial algebras, integration and averaging operators
Li Guo, Markus Rosenkranz, Shanghua Zheng
Rota-Baxter operators are an algebraic abstraction of integration. Following this classical connection, we study the relationship between Rota-Baxter operators and integrals in the…
Classification of Rota-Baxter operators on semigroup algebras of order two and three
Li Guo, Markus Rosenkranz, Shanghua Zheng
In this paper we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices fo…
Relative locations of subwords in free operated semigroups and Motzkin words
Li Guo, Shanghua Zheng
Bracketed words are basic structures both in mathematics (such as Rota-Baxter algebras) and mathematical physics (such as rooted trees) where the locations of the substructures are…
Construction of free commutative integro-differential algebras by the method of Gröbner-Shirshov bases
Xing Gao, Li Guo, Shanghua Zheng
In this paper, we construct a canonical linear basis for free commutative integro-differential algebras by applying the method of Gröbner-Shirshov bases. We establish the Compositi…