31 citations · 64 across the 10 of their papers we have counts for
11 papers
The operad of anti-pre-Lie algebras and its Lie elements
Chengming Bai, Vladimir Dotsenko, Guilai Liu +1
We initiate a systematic operadic approach to anti-pre-Lie algebras. We study the operad controlling anti-pre-Lie algebras, its relationship to the operad of Novikov algebras and i…
The Levi-Civita products of Leibniz algebras with nondegenerate skew-symmetric 2-cocycles
Quan Zhao, Guilai Liu
This paper studies the associated Levi-Civita products of a Leibniz algebra with a nondegenerate skew-symmetric -cocycle. Such products form into the notion of an anti-pre-Leibn…
A further study on averaging commutative and cocommutative infinitesimal bialgebras and special apre-perm bialgebras
Quan Zhao, Guilai Liu
In order to generalize the fact that an averaging commutative algebra gives rise to a perm algebra to the bialgebra level, the notion of a special apre-perm algebra was introduced…
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…
A new approach to the bialgebra theory for relative Poisson algebras
Guilai Liu, Chengming Bai
It is natural to consider extending the typical construction of relative Poisson algebras from commutative differential algebras to the context of bialgebras. The known bialgebra s…
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…
Extending structures for pre-Poisson algebras and pre-Poisson bialgebras
Qianwen Zhu, Guilai Liu, Qinxiu Sun
In this paper, we explore the extending structures problem by the unified product for pre-Poisson algebras. In particular, the crossed product and the factorization problem are inv…
Quasi-triangular, factorizable Leibniz bialgebras and relative Rota-Baxter operators
Chengming Bai, Guilai Liu, Yunhe Sheng +1
We introduce the notion of quasi-triangular Leibniz bialgebras, which can be constructed from solutions of the classical Leibniz Yang-Baxter equation (CLYBE) whose skew-symmetric p…
New splittings of operations of Poisson algebras and transposed Poisson algebras and related algebraic structures
Guilai Liu, Chengming Bai
There are two kinds of splittings of operations, namely, the classical splitting which is interpreted operadically as taking successors and another splitting which we call the seco…
A bialgebra theory for transposed Poisson algebras via anti-pre-Lie bialgebras and anti-pre-Lie-Poisson bialgebras
Guilai Liu, Chengming Bai
The approach for Poisson bialgebras characterized by Manin triples with respect to the invariant bilinear forms on both the commutative associative algebras and the Lie algebras is…
Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebras
Guilai Liu, Chengming Bai
Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebrasWe introduce the notion of anti-pre-Lie algebras as the underlying algebraic structures of nondege…