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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
A bialgebra theory of post-Lie algebras via Manin triples and generalized Hessian Lie groups
Dilei Lu, Chengming Bai, Li Guo
We develop a bialgebra theory of post-Lie algebras that can be characterized by Manin triples of post-Lie algebras associated to a bilinear form satisfying certain invariant condit…
math.QA2024
Solving the Poisson Yang-Baxter equation via deformation-to-quasiclassical-limits
Siyuan Chen, Chengming Bai, Li Guo
A fundamental construction of Poisson algebras is to derive them as the quasiclassical limits (QCLs) of associative algebra deformations of commutative associative algebras. This p…