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arXiv · 1910.04012

String and band complexes over SAG algebras

Andrés Franco·Hernán Giraldo·Pedro Rizzo
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Abstract

We give a combinatorial description of a family of indecomposable objects in the bounded derived categories of a new class of algebras: string almost gentle algebras. These indecomposable objects are, up to isomorphism, the string and band complexes introduced by V. Bekkert and H. Merklen. With this description, we give a necessary and sufficient condition for a given string complex to have infinite minimal projective resolution and we extend this condition for the case of string algebras. Using this characterization we establish a sufficient condition for a string almost gentle algebra (or a string algebra) to have infinite global dimension.

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Andrés Franco, Hernán Giraldo, Pedro Rizzo. 2019-10-09. String and band complexes over SAG algebras. https://arxiv.org/abs/1910.04012

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