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math.RA2026
Para-differential Rota-Baxter algebras and their free objects by Gröbner-Shirshov bases
Li Guo, Aniruddha Talele, Shilong Zhang +1
The algebraic formulation of the derivation and integration related by the First Fundamental Theorem of Calculus (FFTC) gives rise to the notion of differential Rota-Baxter algebra…
math.RA2025
Noncommutative Novikov bialgebras and differential antisymmetric infinitesimal bialgebras with weight
Shanghua Zheng, Yizhen Li, Liushuting Yang +1
This paper first develops a bialgebra theory for a noncommutative Novikov algebra, called a noncommutative Novikov bialgebra, which is further characterized by matched pairs and Ma…
math.RA2024
Extended (tri)dendriform algebras, pre-Lie algebras and post-Lie algebras as companion structures of extended Rota-Baxter algebras
Shanghua Zheng, Shiyu Huang, Li Guo
Under the common theme of splitting of operations, the notions of (tri)dendriform algebras, pre-Lie algebras and post-Lie algebras have attracted sustained attention with broad app…