33 citations · 63 across the 13 of their papers we have counts for
15 papers
Anti-successors and anti-replicators, Manin products and Koszul duality
Chengming Bai, Li Guo, Yunhe Sheng +1
We develop an operadic theory of anti-splitting and anti-replication for binary operads. For a binary operad $\opd$, we define its anti-bisuccessor $\ABSu(\opd)$ and anti-trisucces…
Induced structures of operated algebras with applications to multi-Novikov algebras
Li Guo, Xiaoyan Wang, Huhu Zhang
We provide a general notion of induced structures of operated algebras in the context of unary-binary operads. This notion fully captures the binary quadratic relations encoded by…
General multi-Novikov algebras, multi-differential algebras and their free constructions
Xiaoyan Wang, Li Guo, Huhu Zhang
Motivated by the recent development of noncommutative Novikov algebras and multi-Novikov algebras from the study of regularity structures of stochastic PDEs, this paper gives a gen…
Generalized splitting of algebras with application to a bialgebra structure of Leibniz algebras induced from averaging Lie bialgebras
Chengming Bai, Li Guo, Guilai Liu +1
The classical notion of splitting a binary quadratic operad gives the notion of pre--algebras characterized by -operators, with pre-Lie alge…
Induced structures of averaging commutative and cocommutative infinitesimal bialgebras via a new splitting of perm algebras
Chengming Bai, Li Guo, Guilai Liu +1
It is well-known that an averaging operator on a commutative associative algebra gives rise to a perm algebra. This paper lifts this process to the level of bialgebras. For this pu…
A bialgebra theory of post-Lie algebras via Manin triples and generalized Hessian Lie groups
Dilei Lu, Chengming Bai, Li Guo
We develop a bialgebra theory of post-Lie algebras that can be characterized by Manin triples of post-Lie algebras associated to a bilinear form satisfying certain invariant condit…
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…
On Rota-Baxter vertex operator algebras
Chengming Bai, Li Guo, Jianqi Liu +1
Derivations play a fundamental role in the definition of vertex (operator) algebras, sometimes regarded as a generalization of differential commutative algebras. This paper studies…
Classical Yang-Baxter equation for vertex operator algebras and its operator forms
Chengming Bai, Li Guo, Jianqi Liu
In this paper we introduce an analog of the (classical) Yang-Baxter equation (CYBE) for vertex operator algebras (VOAs) in its tensor form, called the vertex operator Yang-Baxter e…
Post-groups, (Lie-)Butcher groups and the Yang-Baxter equation
Chengming Bai, Li Guo, Yunhe Sheng +1
The notions of a post-group and a pre-group are introduced as a unification and enrichment of several group structures appearing in diverse areas from numerical integration to the…
Infinite-dimensional Lie bialgebras via affinization of Novikov bialgebras and Koszul duality
Yanyong Hong, Chengming Bai, Li Guo
Balinsky and Novikov showed that the affinization of a Novikov algebra naturally defines a Lie algebra, a property that in fact characterizes the Novikov algebra. It is also an ins…
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…