12 citations · 119 across the 39 of their papers we have counts for
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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…
Free Rota-Baxter family algebras and Free (tri)dendriform family algebras
Yuanyuan Zhang, Xing Gao, Dominique Manchon
In this paper, we first construct the free Rota-Baxter family algebra generated by some set in terms of typed angularly -decorated planar rooted trees. As an application, 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…