12 papers
Monoidal structure on Rota-Baxter algebras via augmentation, and free cocycle bialgebras
Li Guo, Yunzhou Xie, Yi Zhang
A tensor product is known for commutative Rota--Baxter algebras through a universal construction, but its underlying algebra need not be the ordinary tensor product an…
The Diagrammar of Quantum Magnusian
Li Guo, Joon-Hwi Kim, Jung-Wook Kim +3
The logarithm of the time-evolution operator has been termed Magnusian, on account of the fact that its expansion describes the Magnus series. The diagrammatic expansion and comput…
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…
Rota-Baxter operators on braces, post-braces and the Yang-Baxter equation
Li Guo, Yan Jiang, Yunhe Sheng +1
Combining the notions of braces and relative Rota-Baxter operators on groups in connection with the Yang-Baxter equation and a factorization theorem of Lie groups from integrable s…
Adjoint motives of modular forms and the Tamagawa number conjecture
Fred Diamond, Matthias Flach, Li Guo
Let be a newform of weight , level with coefficients in a number field , and the adjoint motive of the motive associated to . We carefully discuss th…
Nijenhuis pre-Lie bialgebras, Nijenhuis Lie bialgebras and \sss-equation
Li Guo, Tianshui Ma
We develop a bialgebraic framework for Nijenhuis operators on pre-Lie algebras and coalgebras. Starting from dual triangular pre-Lie bialgebras and weak pseudo-Hessian structures,…
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…
Species of Rota-Baxter algebras by rooted trees, twisted bialgebras and Fock functors
Loic Foissy, Li Guo, Xiao-Song Peng +2
As a fundamental and ubiquitous combinatorial notion, species has attracted sustained interest, generalizing from set-theoretical combinatorial to algebraic combinatorial and beyon…
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…
Rota-Baxter operators, differential operators, pre- and Novikov structures on groups and Lie algebras
Xing Gao, Li Guo, Zongjian Han +1
Rota-Baxter operators on various structures have found important applications in diverse areas, from renormalization of quantum field theory to Yang-Baxter equations. Relative Rota…
Multi-quasisymmetric functions with semigroup exponents, Hopf algebras and Rota-Baxter algebras
Xing Gao, Li Guo, Xiao-Song Peng
Many years ago, G.-C.~Rota discovered a close connection between symmetric functions and Rota-Baxter algebras, and proposed to study generalizations of symmetric functions in the f…
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…