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math.QA2025
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…
math.QA2025★ 1 cited
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…
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…