7 papers
Infinite-dimensional pre-Lie bialgebras induced from Leibniz-dendriform bialgebras and Zinbiel-dendriform bialgebras
Qinxiu Sun
In this paper, we establish a completed pre-Lie bialgebra structure on the tensor product of a Leibniz-dendriform bialgebra and a quadratic -graded Zinbiel algebra. We…
Quasi-triangular, factorizable anti-dendriform bialgebras and relative Rota-Baxter operators
Qinxiu Sun, Min Wu
We introduce the notion of quasi-triangular anti-dendriform bialgebras, which can be induced by the solutions of the AD-YBE whose symmetric parts are invariant. A factorizable anti…
Noncommutative pre-Poisson bialgebras and relative Rota-Baxter operators
Hongliang Li, Qinxiu Sun
In this paper, we develop the bialgebra theory for coherent noncommutative pre-Poisson algebras and establish equivalences among matched pairs, Manin triples, the phase space of no…
Leibniz-dendriform bialgebras and relative Rota-Baxter operators
Qinxiu Sun, Shuangjian Guo
In this paper, we introduce the notion of Leibniz-dendriform bialgebras and establish their equivalence with phase spaces and matched pairs of Leibniz algebras. The study of the co…
Anti-pre-Poisson bialgebras and relative Rota-Baxter operators
Qinxiu Sun, Min Wu
In this paper, we first introduce the notion of an anti-pre-Poisson bialgebra, which is shown to be equivalent to both quadratic anti-pre-Poisson algebras and matched pairs of Pois…
Anti-pre-Novikov algebras, quasi-triangular and factorizable anti-pre-Novikov bialgebras
Qinxiu Sun, Xingyu Zeng
Firstly, we introduce a notion of anti-pre-Novikov algebras as a new framework for decomposing Novikov algebras. Anti-O-operators on Novikov algebras are developed to provide an al…