Exceptional Cycles in the Bounded Derived Categories of Quivers  

作　　者：Peng GUO Pu ZHANG 

机构地区：[1]School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,P.R.C hina

出　　处：《Acta Mathematica Sinica,English Series》2020年第3期207-223,共17页数学学报（英文版）

基　　金：Supported by the NSFC(Grant No.11971304)。

摘　　要：An exceptional n-cycle in a Hom-finite triangulated category with Serre functor has been recently introduced by Broomhead,Pauksztello and Ploog.When n=1,it is a spherical object.We explicitly determine all the exceptional cycles in the bounded derived category D^b(kQ)of a finite quiver Q without oriented cycles.In particular,if Q is an Euclidean quiver,then the length type of exceptional cycles in D^b(kQ)is exactly the tubular type of Q;if Q is a Dynkin quiver of type E_m(m=6,7,8),or Q is a wild quiver,then there are no exceptional cycles in D^b(kQ);and if Q is a Dynkin quiver of type An or D_n,then the length of an exceptional cycle in D^b(kQ)is either h or h/2,where h is the Coxeter number of Q.An exceptional n-cycle in a Hom-finite triangulated category with Serre functor has been recently introduced by Broomhead,Pauksztello and Ploog.When n=1,it is a spherical object.We explicitly determine all the exceptional cycles in the bounded derived category D^b(kQ) of a finite quiver Q without oriented cycles.In particular,if Q is an Euclidean quiver,then the length type of exceptional cycles in D^b(kQ) is exactly the tubular type of Q;if Q is a Dynkin quiver of type E_m(m=6,7,8),or Q is a wild quiver,then there are no exceptional cycles in D^b(kQ);and if Q is a Dynkin quiver of type An or D_n,then the length of an exceptional cycle in D^b(kQ) is either h or h/2,where h is the Coxeter number of Q.

关 键 词：Exceptional CYCLE the Coxeter number the TUBULAR TYPE the LENGTH TYPE 

分 类 号：O153.3[理学—数学]