Silting objects in bounded derived categories of path algebras of quivers of the types bm$A_n$and bm$D_n$

Abstract

It is a basic and difficult 问题 to find all silting objects of a triangulated category. In the case where $A$ is a path algebra of quivers of type $A_n$,this paper gives rules of determining all silting objects of the bounded derived category $D^b(A)$, by which we can find all silting objects of $D^b(A)$ by complicated calculations when $n$ is given. We describe these rules by using the indecomposable two-term presilting objects in $~K^b(\\operatorname{proj}A)$. For a path algebra of quivers of type $D_n$, we do some similar research.