The composite of irreducible morphisms in bounded derived Categories.

CHAIO, CLAUDIA , SOUTO SALORIO M.J. AND TREPODE SONIA.

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Congreso; Colloquie de Algebras non Conmutative.; 2008

Universidade de Sherbrooke.

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 Db(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.