2 citations · 3 across the 6 of their papers we have counts for
6 papers
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…
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…