On Auslander–Reiten components of string complexes for a certain class of symmetric special biserial algebras

Let 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 C of symmetric special biserial algebras, which are indecomposabl...

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Bibliographic Details
Published inBeiträge zur Algebra und Geometrie Vol. 63; no. 4; pp. 707 - 722
Main Authors Giraldo, Hernán, Rueda-Robayo, Ricardo, Vélez-Marulanda, José A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022
Springer Nature B.V
Subjects
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
Original Paper
Strings
16G60
16E05
18G80
16G70
15A21
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Summary:Let 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 C of symmetric special biserial algebras, which are indecomposable perfect complexes in the corresponding derived category. We also prove that if Λ is a k -algebra in the class C and P ∙ is a string complex over Λ , then P ∙ lies in the rim of its Auslander–Reiten component.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-021-00607-x