On the quiver with relations of a quasitilted algebra and applications. Issue 9 (2nd September 2017)

• Record Type: Journal Article
• Authors: Bordino, Natalia; Fernández, Elsa; Trepode, Sonia
• Is Part Of: Communications in algebra. Volume 45:Issue 9(2017)
• Page Start: 4050
• Page End: 4061
• Publication Date: 2017-09-02
• Subjects: Bounded consecutive relations -- strongly simply connected -- tilting -- quasitilted; Primary 16G20 -- Secondary 16G70; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1259417
• Languages: English
• ISSNs: 0092-7872

Abstract

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 .