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math.RA2025
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…
math.RA2025
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…
math.RA2025
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…