On the quiver with relations of a quasitilted algebra and applications

Abstract

In this paper we discuss, in terms of quiver with relations,sufficient and necessary conditions for an algebra to be a quasitiltedalgebra. We start with an algebra with global dimension at most twoand we give a sufficient condition to be a quasitilted algebra. We showthat this condition is not necessary. In the case of a strongly simply con-nected schurian algebra, we discuss necessary conditions, and combiningboth type of conditions, we are able to analyze if some given algebra isquasitilted. As an application we obtain the quiver with relations of allthe tilted and cluster tilted algebras of Dynkin type Ep.