On the quiver with relations of a quasitilted algebra and applications. Issue 9 (2nd September 2017) - Bordino, Natalia; Fernández, Elsa; Trepode, Sonia
ABSTRACT: In this paper we discuss, in terms of quiver with relations, suﬃcient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension at most two and we give a suﬃcient condition to be a quasitilted algebra. We show that this condition is not necessary. In the case of a strongly simply connected schurian algebra, we discuss necessary conditions, and combining both types of conditions, we are able to analyze if some given algebra is quasitilted. As an application we obtain the quiver with relations of all the tilted and cluster tilted algebras of Dynkin type E p .