【摘 要】
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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
【机 构】
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School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, P.R.China
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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 Db(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 Db(kQ) is exactly the tubular type of Q;if Q is a Dynkin quiver of type Em (m =6,7,8),or Q is a wild quiver,then there are no exceptional cycles in Db(kQ);and if Q is a Dynkin quiver of type An or Dn,then the length of an exceptional cycle in Db(kQ) is either h or h/2,where h is the Coxeter number of Q.
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