3 citations · 3 across the 12 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…
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…