3 citations · 3 across the 12 of their papers we have counts for
14 papers
Disuccessors, Gröbner-Shirshov bases and free L-dendriform algebras
Huhu Zhang, Xing Gao, Yuanyuan Zhang
In this paper, we prove respectively that the disuccessor operations on the associative operad $\as$, the Lie operad $\lie$, and the pre-Lie operad $\prelie$ preserve Gröbner-Shirs…
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…
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…
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…
Weighted differential (-tri)dendriform algebras
Yuanyuan Zhang, Huhu Zhang, Tingzeng Wu +1
In this paper, we first introduce a weighted derivation on algebras over an operad , and prove that for the free -algebra, its weighted derivation is determined by…
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…
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…
Free weighted differential (-tri)dendriform algebras
Yuanyuan Zhang, Huhu Zhang, Tingzeng Wu +1
In the present paper, we propose the concepts of weighted differential (-tri)dendriform algebras and give some basic properties of them. The corresponding free objects are const…
Free -Rota-Baxter systems and Gröbner-Shirshov bases
Yuanyuan Zhang, Huhu Zhang, Xing Gao
In this paper, we propose the concept of an -Rota-Baxter system, which is a generalization of a Rota-Baxter system and an -Rota-Baxter algebra of weight zero. In the framewor…
Operator identities on Lie algebras, rewriting systems and Gröbner-Shirshov bases
Huhu Zhang, Xing Gao, Li Guo
Motivated by the pivotal role played by linear operators, many years ago Rota proposed to determine algebraic operator identities satisfied by linear operators on associative algeb…
Rota's program on algebraic operators, rewriting systems and Gröbner-Shirshov bases
Xing Gao, Li Guo, Huhu Zhang
Many years ago, Rota proposed a program on determining algebraic identities that can be satisfied by linear operators. After an extended period of dormant, progress on this program…
Free weighted (modified) differential algebras, free (modified) Rota-Baxter algebras and Gröbner-Shirshov bases
Zhicheng Zhu, Huhu Zhang, Xing Gao
In this paper, we obtain respectively some new linear bases of free unitary (modified) weighted differential algebras and free nonunitary (modified) Rota-Baxter algebras, in terms…
Compatible structures on unary binary nonsymmetric operads with quadratic and cubic relations
Xing Gao, Li Guo, Huhu Zhang
Various compatibility conditions among replicated copies of operations in a given algebraic structure have appeared in broad contexts in recent years. Taking an uniform approach, t…