31 citations · 64 across the 10 of their papers we have counts for
5 papers · 1 filter
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…
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…