String and band complexes over SAG algebras
Representation Theory
2020-10-12 v3 Category Theory
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.
Cite
@article{arxiv.1910.04012,
title = {String and band complexes over SAG algebras},
author = {Andrés Franco and Hernán Giraldo and Pedro Rizzo},
journal= {arXiv preprint arXiv:1910.04012},
year = {2020}
}
Comments
We have added new examples. Also, we have renewed some proofs and corrected minor typos