5 citations · 12 across the 5 of their papers we have counts for
5 papers
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…
Left counital Hopf algebras on free Nijenhuis algebras
Xing Gao, Peng Lei, Tianjie Zhang
Factorization in algebra is an important problem. In this paper, we first obtain a unique factorization in free Nijenhuis algebras. By using of this unique factorization, we then d…
Hopf algebras of rooted forests, cocyles and free Rota-Baxter algebras
Xing Gao, Li Guo, Tianjie Zhang
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum fie…
Bialgebra and Hopf algebra structures on free Rota-Baxter algebras
Xing Gao, Li Guo, Tianjie Zhang
In this paper, we obtain a canonical factorization of basis elements in free Rota-Baxter algebras built on bracketed words. This canonical factorization is applied to give a coalge…
Averaging algebras, rewriting systems and Grbner-Shirshov bases
Xing Gao, Tianjie Zhang
In this paper, we study the averaging operator by assigning a rewriting system to it. We obtain some basic results on the kind of rewriting system we used. In particular, we obtain…