On the quiver with relations of a quasitilted algebra and applications

2014/04/22 by Natalia Bordino, Bordino, Natalia, Elsa Fernández +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum many-body systems #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1404.5294

openalex publication_date 2014/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we discuss, in terms of quivers with relations, sufficient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension two and we give a sufficient condition for it 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 type of conditions, we are able to analyze if the 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.

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