Truncation Ideals Of The Associative Algebra Operad And Poisson Operad

Operad theory originates from the study of homotopy in algebraic topology.In recent years,the study of operad's own algebraic structure has been widely concerned.The associative algebra operad Ass and Poisson operad Pois are two common types of operad,whose algebraic structure can be used to solve problems of their related algebra.For instance,the ideal of associative algebra operad is closely related to the polynomial identity algebra,whose determination of generators is important for the research of the polynomial identity algebra.Additionally,as a right S-module,Poisson operad and associative algebra operad have many similar qualities.This thesis consists of the following three parts:In the first chapter,we mainly introduce the research background and significance,and then introduce the preliminaries,main questions and results in this thesis.In Chapter 2,we review the definition and properties of associative algebra operad and Poisson operad,then introduce properties of its truncation ideal and the definition of finite generation.In Chapter 3,we list some preparatory works before proving the main content firstly,and then prove that the k-th truncation ideal,k?,of the associative algebra operad can be generated by k?(k+2)or k?(k+1)U k+1?(k+2)by induction.And we can figure out the generators of poisson operad's truncation ideal analogically.