Composite of irreducible morphisms in the bounded derived Category.

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

Sao Pedro

Conferencia; International Conference of Representations of Algebras; 2008

Universidad de Sao Paulo. Brasil.

In this work, we study the composite of two irreducible morphisms in the bounded derived category of the finitely generated modules over an artin algebra of finite global dimension. We find necessary and sufficient conditions such that their composite is different from zero and belongs to radical cube. We also study when the composite of n-irreducible morphisms in the bounded derived category of the finitely generated modules of a finite dimensional hereditary algebra over an algebraically closed field, is non zero and belongs to a greater power of the radical. We apply these results to cluster tilted algebras.