8 papers
Induced structures of operated algebras with applications to multi-Novikov algebras
Li Guo, Xiaoyan Wang, Huhu Zhang
We provide a general notion of induced structures of operated algebras in the context of unary-binary operads. This notion fully captures the binary quadratic relations encoded by…
General multi-Novikov algebras, multi-differential algebras and their free constructions
Xiaoyan Wang, Li Guo, Huhu Zhang
Motivated by the recent development of noncommutative Novikov algebras and multi-Novikov algebras from the study of regularity structures of stochastic PDEs, this paper gives a gen…
Some new operated Lie polynomial identities and Gröbner-Shirshov bases
Huhu Zhang, Xing Gao, Tingzeng Wu +1
Bremner and Elgendy developed a classification of operated polynomial identities for linear operators on associative algebras, encompassing both classical and newly discovered case…
Averaging operators on groups and Hopf algebras
Huhu Zhang, Xing Gao
Rota-Baxter operators on groups were studied quite recently. Motivated mainly by the fact that weight zero Rota-Baxter operators and averaging operators are Koszul dual to each oth…
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…
Compatible structures of operads by polarization, their Koszul duality and Manin products
Huhu Zhang, Xing Gao, Li Guo
Algebraic structures with multiple copies of a given type of operations interrelated by various compatibility conditions have long being studied in mathematics and mathematical phy…