12 citations · 119 across the 39 of their papers we have counts for
6 papers · 1 filter
Reynolds algebras and their free objects from bracketed words and rooted trees
Tianjie Zhang, Xing Gao, Li Guo
The study of Reynolds algebras has its origin in the well-known work of O. Reynolds on fluid dynamics in 1895 and has since found broad applications. It also has close relationship…
A note on connected cofiltered coalgebras, conilpotent coalgebras and Hopf algebras
Xing Gao, Li Guo
This notes gives a proof that a connected coaugmented cofiltered coalgebra is a conilpotent coalgebra and thus a connected coaugmented cofiltered bialgebra is a Hopf algebra. This…
Free (tri)dendriform family algebras
Yuanyuan Zhang, Xing Gao, Dominique Manchon
In this paper, we first prove that a Rota-Baxter family algebra indexed by a semigroup induces an ordinary Rota-Baxter algebra structure on the tensor product with the semigroup al…
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…
Free modified Rota-Baxter algebras and Hopf algebras
Xigou Zhang, Xing Gao, Li Guo
The notion of a modified Rota-Baxter algebra comes from the combination of those of a Rota-Baxter algebra and a modified Yang-Baxter equation. In this paper, we first construct fre…