Abstract
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.
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Acknowledgements
This paper was prepared for the proceedings of the meeting Geometry in Algebra and Algebra in Geometry, GAAG-V, held in Medellín in 2019. The first author would like to thank the organizers for the invitation to speak and to Colciencias (Beca Doctorado Nacional Colciencias, Convocatoria 647 de 2014). The authors are also grateful to CODI (Universidad de Antioquia, U de A). The GAAG-V and the third author, were partially supported by CODI, University of Antioquia, project 2017-15756 Stable Limit Linear Series on Curves.
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Communicated by Kostiantyn Iusenko.
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Franco, A., Giraldo, H. & Rizzo, P. Periodic string complexes over string algebras. São Paulo J. Math. Sci. 15, 695–719 (2021). https://doi.org/10.1007/s40863-020-00202-3
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DOI: https://doi.org/10.1007/s40863-020-00202-3