9 citations · 9 across the 11 of their papers we have counts for
11 papers
Factorizable Lie conformal bialgebras, quadratic Rota-Baxter Lie conformal algebras and some induced structures
Zhongyin Xu, Chengming Bai, Yanyong Hong
We introduce the notion of factorizable Lie conformal bialgebras and establish their correspondence with quadratic Rota-Baxter Lie conformal algebras of nonzero weight. Consequentl…
Controlling graded Lie algebras and cohomologies of double Lie algebras
Zhongyin Xu, Chengming Bai
We construct a graded Lie algebra structure on the space of cyclically skew-symmetric cochains whose Maurer-Cartan elements characterize double Lie algebra structures. Twisting by…
Poisson bialgebras by deformations-to-quasiclassical limits
Siyuan Chen, Chengming Bai
Poisson algebras are the quasiclassical limits of associative algebra deformations of commutative associative algebras. This paper extends this process to the level of bialgebras.…
Leibniz conformal bialgebras and the classical Leibniz conformal Yang-Baxter equation
Zhongyin Xu, Chengming Bai, Yanyong Hong
We introduce the notion of Leibniz conformal bialgebras, presenting a bialgebra theory for Leibniz conformal algebras as well as the conformal analogues of Leibniz bialgebras. They…
Quantizations of transposed Poisson algebras by Novikov deformations
Siyuan Chen, Chengming Bai
The notions of the Novikov deformation of a commutative associative algebra and the corresponding classical limit are introduced. We show such a classical limit belongs to a subcla…
On Poisson conformal bialgebras
Yanyong Hong, Chengming Bai
We develop a conformal analog of the theory of Poisson bialgebras as well as a bialgebra theory of Poisson conformal algebras. We introduce the notion of Poisson conformal bialgebr…
Solving the Poisson Yang-Baxter equation via deformation-to-quasiclassical-limits
Siyuan Chen, Chengming Bai, Li Guo
A fundamental construction of Poisson algebras is to derive them as the quasiclassical limits (QCLs) of associative algebra deformations of commutative associative algebras. This p…
Deformation families of Novikov bialgebras via differential antisymmetric infinitesimal bialgebras
Yanyong Hong, Chengming Bai, Li Guo
Generalizing S. Gelfand's classical construction of a Novikov algebra from a commutative differential algebra, a deformation family , for scalars , of Novikov algeb…
A bialgebra theory of Gel'fand-Dorfman algebras with applications to Lie conformal bialgebras
Yangyon Hong, Chengming Bai, Li Guo
Gel'fand-Dorfman algebras (GD algebras) give a natural construction of Lie conformal algebras and are in turn characterized by this construction. In this paper, we define the Gel'f…
Parity duality of super -matrices via -operators and pre-Lie superalgebras
Chengming Bai, Li Guo, Runxuan Zhang
This paper studies super -matrices and operator forms of the super classical Yang-Baxter equation. First by a unified treatment, the classical correspondence between -matrice…
Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras
C. Bai, R. Bai, L. Guo +1
We introduce a dual notion of the Poisson algebra by exchanging the roles of the two binary operations in the Leibniz rule defining the Poisson algebra. We show that the transposed…