10 citations · 57 across the 16 of their papers we have counts for
16 papers
Species of Rota-Baxter algebras by rooted trees, twisted bialgebras and Fock functors
Loic Foissy, Li Guo, Xiao-Song Peng +2
As a fundamental and ubiquitous combinatorial notion, species has attracted sustained interest, generalizing from set-theoretical combinatorial to algebraic combinatorial and beyon…
Rota-Baxter operators, differential operators, pre- and Novikov structures on groups and Lie algebras
Xing Gao, Li Guo, Zongjian Han +1
Rota-Baxter operators on various structures have found important applications in diverse areas, from renormalization of quantum field theory to Yang-Baxter equations. Relative Rota…
Twisted Mahler discrete residues
Carlos E. Arreche, Yi Zhang
Recently we constructed Mahler discrete residues for rational functions and showed they comprise a complete obstruction to the Mahler summability problem of deciding whether a give…
Extending structures of Rota-Baxter Lie algebras
Xiao-song Peng, Yi Zhang
In this paper, we first introduce the notion of an extending datum of a Rota-Baxter Lie algebra through a vector space. We then construct a unified product for the Rota-Baxter Lie…
Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras
Xing Gao, Li Guo, Yi Zhang
The Rota-Baxter algebra and the shuffle product are both algebraic structures arising from integral operators and integral equations. Free commutative Rota-Baxter algebras provide…
Operator forms of nonhomogeneous associative classical Yang-Baxter equation
Chengming Bai, Xing Gao, Li Guo +1
This paper studies operator forms of the nonhomogeneous associative classical Yang-Baxter equation (nhacYBe), extending and generalizing such studies for the classical Yang-Baxter…
Matching Hom-Setting of Rota-Baxter algebras, dendriform algebras and pre-Lie algebras
Dan Chen, Xiao-Song Peng, Chia Zargeh +1
In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras and matching (pre)Lie algebras. Moreover, we…
Hopf algebra of multi-decorated rooted forests, free matching Rota-Baxter algebras and Gröbner-Shirshov bases
Xing Gao, Li Guo, Yi Zhang
Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study of algebraic structures with replicating operations. To understand t…
Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
Xing Gao, Li Guo, Yi Zhang
We introduce the notion of a matching Rota-Baxter algebra motivated by the recent work on multiple pre-Lie algebras arising from the study of algebraic renormalization of regularit…
Hopf algebras of planar binary trees: an operated algebra approach
Yi Zhang, Xing Gao
Parallel to operated algebras built on top of planar rooted trees via the grafting operator , we introduce and study -algebras and more generally -algebras based…
Weighted infinitesimal unitary bialgebras, pre-Lie, matrix algebras and polynomial algebras
Yi Zhang, Jiawen Zheng, Yanfeng Luo
Motivated by the classical comatrix coalgebra, we introduce the concept of a Newtonian comatrix coalgebra. We construct an infinitesimal unitary bialgebra on a matrix algebra and a…
Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles
Yi Zhang, Dan Chen, Xing Gao +1
In this paper, we define a new coproduct on the space of decorated planar rooted forests to equip it with a weighted infinitesimal unitary bialgebraic structure. We introduce the c…
Weighted infinitesimal unitary bialgebras on matrix algebras and weighted associative Yang-Baxter equations
Yi Zhang, Xing Gao, Jia-wen Zheng
We equip a matrix algebra with a weighted infinitesimal unitary bialgebraic structure, via a construction of a suitable coproduct. Furthermore, an infinitesimal unitary Hopf algebr…
Weighted infinitesimal bialgebras
Xing Gao, Yi Zhang
As an algebraic meaning of the nonhomogenous associative Yang-Baxter equation, weighted infinitesimal bialgebras play an important role in mathematics and mathematical physics. In…
Contraction of Ore Ideals with Applications
Yi Zhang
Ore operators form a common algebraic abstraction of linear ordinary differential and recurrence equations. Given an Ore operator with polynomial coefficients in , it genera…
Primitive orthogonal idempotents of Brandt semigroup algebras
Yi Zhang, Jian-Rong Li, Xiao-Song Peng +1
A complete set of primitive orthogonal idempotents plays an important role in the representation theory of an associative algebra. In this paper, we construct a complete set of pri…