10 citations · 31 across the 13 of their papers we have counts for
13 papers
Rota-Baxter operators on cocommutative Hopf algebras and Hopf braces
Huihui Zheng, Li Guo, Tianshui Ma +1
This paper studies the relationship of Rota-Baxter operators on cocommutative Hopf algebras with Hopf braces and the Yang-Baxter equation, with emphasis on the embedding of cocommu…
Rota-Baxter Lie bialgebras, classical Yang-Baxter equations and special L-dendriform bialgebras
Chengming Bai, Li Guo, Guilai Liu +1
We establish a bialgebra structure on Rota-Baxter Lie algebras following the Manin triple approach to Lie bialgebras. Explicitly, Rota-Baxter Lie bialgebras are characterized by ge…
Double crossed biproducts and related structures
Tianshui Ma, Jie Li, Haiyan Yang +1
Let be a bialgebra. Let be a linear map, where is a left -comodule coalgebra, and an algebra with a left -weak action . Let $τ: H…
Transposed BiHom-Poisson algebras
Tianshui Ma, Bei Li
In this paper, we introduce the concept of transposed BiHom-Poisson (abbr. TBP) algebras which can be constructed by the BiHom-Novikov-Poisson algebras. Several useful identities f…
Bialgebras, Frobenius algebras and associative Yang-Baxter equations for Rota-Baxter algebras
Chengming Bai, Li Guo, Tianshui Ma
Rota-Baxter operators and bialgebras go hand in hand in their applications, such as in the Connes-Kreimer approach to renormalization and the operator approach to the classical Yan…
Nonhomogeneous associative Yang-Baxter equations
Tianshui Ma, Jie Li
We introduce the notion of associative (BiHom-)Yang-Baxter pair of weight which can provide the solution to the double curved Rota-Baxter (BiHom-)system. Equivalent charact…
On the tensor product of two oriented quantum algebras
Tianshui Ma, Haiyang Yang, Tao Yang
In this paper, we give the oriented quantum algebra (abbr. OQA) structures on the tensor product of two different OQAs by using Chen's weak -matrix in [J. Algebra 204…
Rota-Baxter operators on Turaev's Hopf group (co)algebras I: Basic definitions and related algebraic structures
Tianshui Ma, Jie Li, Liangyun Chen +1
We find a natural compatible condition between the Rota-Baxter operator and Turaev's (Hopf) group-(co)algebras, which leads to the concept of Rota-Baxter Turaev's (Hopf) group-(co)…
Hopf brace, braid equation and bicrossed coproduct
Huihui Zheng, Fangshu Li, Tianshui Ma +1
In this paper, we mainly give some equivalent characterisations of Hopf braces, show that the category of Hopf braces is equivalent to the category $\mathcal{C}(A…
Rota-Baxter bisystems and covariant bialgebras
Tianshui Ma, Abdenacer Makhlouf, Sergei Silvestrov
The aim of this paper is first to introduce and study Rota-Baxter cosystems and bisystems as generalization of Rota-Baxter coalgebras and bialgebras, respectively, with various exa…
Curved O-operator systems
Tianshui Ma, Abdenacer Makhlouf, Sergei Silvestrov
In this paper, we introduce the notion of curved -operator systems as a generalization of T. Brzeziński's (curved) Rota-Baxter systems, and then investigate their rela…
Cobraided Smash Product Hom-Hopf Algebras
Tianshui Ma, Haiying Li, Tao Yang
Let $(A,\a)$ and $(B,\b)$ be two Hom-Hopf algebras. In this paper, we construct a class of new Hom-Hopf algebras: -smash product $(A\natural_R B,\aø\b)$. Moreover, necessary and…
Rota-Baxter coalgebras and Rota-Baxter bialgebras
Tianshui Ma, Linlin Liu
We give a construction of Rota-Baxter coalgebras from Hopf module coalgebras and also derive the structures of the pre-Lie coalgebras via Rota-Baxter coalgebras of different weight…