68 citations · 246 across the 15 of their papers we have counts for
15 papers
An algebraic formulation of the locality principle in renormalisation
Pierre Clavier, Li Guo, Sylvie Paycha +1
We study the mathematical structure underlying the concept of locality which lies at the heart of classical and quantum field theory, and develop a machinery used to preserve local…
On Rings of Differential Rota-Baxter Operators
Xing Gao, Li Guo, Markus Rosenkranz
Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying th…
A conical approach to Laurent expansions for multivariate meromorphic germs with linear poles
Li Guo, Sylvie Paycha, Bin Zhang
We use convex polyhedral cones to study a large class of multivariate meromorphic germs, namely those with linear poles, which naturally arise in various contexts in mathematics an…
Free integro-differential algebras and Gröbner-Shirshov bases
Xing Gao, Li Guo, Markus Rosenkranz
The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative an…
Applications of shuffle product to restricted decomposition formulas for multiple zeta values
Li Guo, Peng Lei, Biao Ma
In this paper we obtain a recursive formula for the shuffle product and apply it to derive two restricted decomposition formulas for multiple zeta values (MZVs). The first formula…
Constructions of free commutative integro-differential algebras
Xing Gao, Li Guo
In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras b…
On Integro-Differential Algebras
Li Guo, Georg Regensburger, Markus Rosenkranz
The concept of integro-differential algebra has been introduced recently in the study of boundary problems of differential equations. We generalize this concept to that of integro-…
Polylogarithms and multiple zeta values from free Rota-Baxter algebras
Li Guo, Bin Zhang
We show that the shuffle algebras for polylogarithms and regularized MZVs in the sense of Ihara, Kaneko and Zagier are both free commutative nonunitary Rota-Baxter algebras with on…
Structure of Hochschild cohomology of path algebras and differential formulation of Euler's polyhedron formula
Li Guo, Fang Li
This article studies the Lie algebra of derivations on the path algebra of a quiver and the Lie algebra on the first Hochschild cohomology group . We r…
Algebraic Birkhoff decomposition and its applications
Li Guo
Central in the Hopf algebra approach to the renormalization of perturbative quantum field theory of Connes and Kreimer is their Algebraic Birkhoff Decomposition. In this tutorial a…
Operated semigroups, Motzkin paths and rooted trees
Li Guo
Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an…
Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
Kurusch Ebrahimi-Fard, Li Guo
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into com…
Multiple zeta values and Rota--Baxter algebras
Kurusch Ebrahimi-Fard, Li Guo
We study multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on mult…
Free Rota-Baxter algebras and rooted trees
Kurusch Ebrahimi-Fard, Li Guo
A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota-Baxter relation, that generalizes the integration…
Coherent Unit Actions on Operads and Hopf Algebras
Kurusch Ebrahimi-Fard, Li Guo
Coherent unit actions on a binary, quadratic operad were introduced by Loday and were shown by him to give Hopf algebra structures on the free algebras when the operad is also regu…