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 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.

KEYWORDS:

• Bounded consecutive relations
• strongly simply connected
• tilting
• quasitilted

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 16G20
• Secondary 16G70

Acknowledgment

We thank M. I. Platzeck for useful discussions about Theorem 4.3. This work is part of the Ph.D Thesis of Natalia Bordino, under the supervision of her advisers, Sonia Trepode and Elsa Fernández.