12 papers
Bialgebra theory, the Yang-Baxter equation and relative Rota-Baxter operators for diassociative algebras
Hui Hu, Yizhen Li, Guilai Liu +1
In this paper, we develop a bialgebra theory for diassociative algebras. Inspired by the notion of a quadratic diassociative algebra, we introduce the concept of a Manin triple of…
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…
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…
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…
Extended Rota-Baxter algebras, diagonally colored Delannoy paths and Hopf algebras
Shanghua Zheng, Li Guo, Huizhen Qiu
The Rota-Baxter operator and the modified Rota-Baxter operator on various algebras are both important in mathematics and mathematical physics. The former is originated from the int…
Construction of free quasi-idempotent differential Rota-Baxter algebras by Gröbner-Shirshov bases
Huizhen Qiu, Shanghua Zheng, Yangfan Dan
Differential operators and integral operators are linked together by the first fundamental theorem of calculus. Based on this principle, the notion of a differential Rota-Baxter al…