2020/06/23 by Franco, Andrés, Giraldo, Hernán, Rizzo, Pedro
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2006.14386
In this paper we develop combinatorial techniques for the case of string algebras with the aim to give a characterization of string complexes with infinite minimal projective resolution. These complexes will be called periodic string complexes. As a consequence of this characterization, we give two important applications. The first one, is a sufficient condition for a string algebra to have infinite global dimension. In the second one, we exhibit a class of indecomposable objects in the derived category for a special case of string algebras. Every construction, concept and consequence in this paper is followed by some illustrative examples.