Singularity categories of derived categories of hereditary algebras are derived categories

We show that for the path algebra A of an acyclic quiver, the singularity category of the derived category Db(modA) is triangle equivalent to the derived category of the functor category of mod_A, that is, Dsg(Db(modA))≃Db(mod(mod_A)). This extends a result in [14] for the path algebra A of a Dynkin...

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Bibliographic Details
Published inJournal of pure and applied algebra Vol. 224; no. 2; pp. 836 - 859
Main Author Kimura, Yuta
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2020
Subjects
Dualizing variety
Functor category
Hereditary algebra
Repetitive category
Tilting subcategory
16E30
18A25
Functor category
Dualizing variety
Tilting subcategory
Repetitive category
Hereditary algebra
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Summary:We show that for the path algebra A of an acyclic quiver, the singularity category of the derived category Db(modA) is triangle equivalent to the derived category of the functor category of mod_A, that is, Dsg(Db(modA))≃Db(mod(mod_A)). This extends a result in [14] for the path algebra A of a Dynkin quiver. An important step is to establish a functor category analog of Happel's triangle equivalence for repetitive algebras.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2019.06.013