4 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…
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…