Singularity categories of derived categories of hereditary algebras are derived categories

Kimura Y (2020)
JOURNAL OF PURE AND APPLIED ALGEBRA 224(2): 836-859.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck| Englisch
 
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Abstract / Bemerkung
We show that for the path algebra A of an acyclic quiver, the singularity category of the derived category D-b(modA) is triangle equivalent to the derived category of the functor category of mod A, that is, D-sg (D-b(modA)) similar or equal to D-b(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. (C) 2019 Elsevier B.V. All rights reserved.
Stichworte
Functor category; Repetitive category; Hereditary algebra; Tilting; subcategory; Dualizing variety
Erscheinungsjahr
2020
Zeitschriftentitel
JOURNAL OF PURE AND APPLIED ALGEBRA
Band
224
Ausgabe
2
Seite(n)
836-859
ISSN
0022-4049
eISSN
1873-1376
Page URI
https://pub.uni-bielefeld.de/record/2938372

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Kimura Y. Singularity categories of derived categories of hereditary algebras are derived categories. JOURNAL OF PURE AND APPLIED ALGEBRA. 2020;224(2):836-859.
Kimura, Y. (2020). Singularity categories of derived categories of hereditary algebras are derived categories. JOURNAL OF PURE AND APPLIED ALGEBRA, 224(2), 836-859. doi:10.1016/j.jpaa.2019.06.013
Kimura, Y. (2020). Singularity categories of derived categories of hereditary algebras are derived categories. JOURNAL OF PURE AND APPLIED ALGEBRA 224, 836-859.
Kimura, Y., 2020. Singularity categories of derived categories of hereditary algebras are derived categories. JOURNAL OF PURE AND APPLIED ALGEBRA, 224(2), p 836-859.
Y. Kimura, “Singularity categories of derived categories of hereditary algebras are derived categories”, JOURNAL OF PURE AND APPLIED ALGEBRA, vol. 224, 2020, pp. 836-859.
Kimura, Y.: Singularity categories of derived categories of hereditary algebras are derived categories. JOURNAL OF PURE AND APPLIED ALGEBRA. 224, 836-859 (2020).
Kimura, Yuta. “Singularity categories of derived categories of hereditary algebras are derived categories”. JOURNAL OF PURE AND APPLIED ALGEBRA 224.2 (2020): 836-859.