3 citations · 7 across the 8 of their papers we have counts for
8 papers
Nijenhuis modules and the ring of Nijenhuis operators
Shilong Zhang, Xiao-Song Peng, Liuqing Dong
In this paper, we study the Nijenhuis modules of Nijenhuis algebras. The concepts of free, projective, injective, and flat Nijenhuis modules are introduced, and a construction of f…
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…
Integro-differential rings on species and derived structures
Xing Gao, Li Guo, Markus Rosenkranz +2
In the theory of species, differential as well as integral operators are known to arise in a natural way. In this paper, we shall prove that they precisely fit together in the alge…
Rota-Baxter Lie -algebras
Shilong Zhang, Jiefeng Liu
In this paper, we introduce the notion of Rota-Baxter Lie -algebras, which is a categorification of Rota-Baxter Lie algebras. We prove that the category of Rota-Baxter Lie -a…
Cohomologies and deformations of pre-Lie-morphism triples
Yibo Wang, Shilong Zhang, Jiefeng Liu
A (pre-)Lie-morphism triple consists of two (pre-)Lie algebras and a (pre-)Lie algebra homomorphism between them. We give chomologies of pre-Lie-morphism triples. As an application…
Classification of operator extensions, monad liftings and distributive laws for differential algebras and Rota-Baxter algebras
Shilong Zhang, Li Guo, William Keigher
Generalizing the algebraic formulation of the First Fundamental Theorem of Calculus (FFTC), a class of constraints involving a pair of operators was considered in \cite{ZGK2}. For…
Extensions of Operators, Liftings of Monads and Distributive Laws
Li Guo, William Keigher, Shilong Zhang
In a previous study, the algebraic formulation of the First Fundamental Theorem of Calculus (FFTC) is shown to allow extensions of differential and Rota-Baxter operators on the one…
Monads and distributive laws for Rota-Baxter and differential algebras
Li Guo, William Keigher, Shilong Zhang
In recent years, algebraic studies of the differential calculus and integral calculus in the forms of differential algebra and Rota-Baxter algebra have been merged together to refl…