182 citations · 1.3k across the 103 of their papers we have counts for
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Renormalization of quasisymmetric functions
Li Guo, Houyi Yu, Bin Zhang
As a natural basis of the Hopf algebra of quasisymmetric functions, monomial quasisymmetric functions are formal power series defined from compositions. The same definition applies…
Integration and geometrization of Rota-Baxter Lie algebras
Li Guo, Honglei Lang, Yunhe Sheng
This paper first introduces the notion of a Rota-Baxter operator (of weight ) on a Lie group so that its differentiation gives a Rota-Baxter operator on the corresponding Lie al…
Construction of free differential algebras by extending Gröbner-Shirshov bases
Li Guo, Yunnan Li
As a fundamental notion, the free differential algebra on a set is concretely constructed as the polynomial algebra on the differential variables. Such a construction is not known…
An algebraic study of Volterra integral equations and their operator linearity
Li Guo, Richard Gustavson, Yunnan Li
The algebraic study of special integral operators led to the notions of Rota-Baxter operators and shuffle products which have found broad applications. This paper carries out an al…
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…