Composite of irreducible morphisms in the bounded derived category

Abstract

We study necessary and sufficient conditions for the existence of n irreducible morphisms in the bounded derived category of an Artin algebra, with non-zero composite in the n + 1 -power of the radical. In the case of D b ( H ) , the bounded derived category of an Ext-finite hereditary k -category with tilting object, such irreducible morphisms exist if and only if H is derived equivalent to a wild hereditary algebra or to a wild canonical algebra. We also characterize the cluster tilted algebras having such irreducible morphisms.