Abstract
Let \(\mathbb {k}\) be an algebraically closed field. In this article, inspired by the description of indecomposable objects in the derived category of a gentle algebra obtained by Bekkert and Merklen, we define string complexes for a certain class \({\mathscr {C}}\) of symmetric special biserial algebras, which are indecomposable perfect complexes in the corresponding derived category. We also prove that if \(\Lambda \) is a \(\mathbb {k}\)-algebra in the class \({\mathscr {C}}\) and \(P^\bullet \) is a string complex over \(\Lambda \), then \(P^\bullet \) lies in the rim of its Auslander–Reiten component.
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This research was partly supported by the Faculty Scholarship of the Office of Academic Affairs at the Valdosta State University, by CODI and Estrategia de Sostenibilidad 2020-2021 (Universidad de Antioquia, UdeA), and COLCIENCIAS (CONVOCATORIA DOCTORADOS NACIONALES N0. 727 de 2015).
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Giraldo, H., Rueda-Robayo, R. & Vélez-Marulanda, J.A. On Auslander–Reiten components of string complexes for a certain class of symmetric special biserial algebras. Beitr Algebra Geom 63, 707–722 (2022). https://doi.org/10.1007/s13366-021-00607-x
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DOI: https://doi.org/10.1007/s13366-021-00607-x