Operadic Rota's Classification Problem

Differential operators and Rota-Baxter operators play an important role in mathematics.The famous combinatorist Rota put forward the problem of Rota's Classification Problem: finding out the algebraic identities that can be satisfied by a linear operator on algebra.Rota's Classification Problem on associative algebras has been studied in the context of Gr?bner-Shirshov bases and rewriting systems by Xing Gao and Li Guo [6].There they accurately described the meaning of Rota's Classification Problem and found a new linear operator.Rota's Classification Problem can also be posed for other algebraic structures,such as Lie algebras and dendriform algebras.In this paper,we raise Rota's Classification Problem to the level of operad.We study operadic version of Rota's Classification Problem by the method of Gr?bner-Shirshov bases and rewriting systems.This research will promote the study of non-connected operads.