From submodule categories to the stable Auslander algebra

Eiriksson Ö (2017)
JOURNAL OF ALGEBRA 486: 98-118.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We construct two functors from the submodule category of a representation-finite self-injective algebra A to the module category of the stable Auslander algebra of A. These functors factor through the module category of the Auslander algebra of A. Moreover they induce equivalences from the quotient categories of the submodule category modulo their respective kernels and said kernels have finitely many indecomposable objects up to isomorphism. Their construction uses a recollement of the module category of the Auslander algebra induced by an idempotent and this recollement determines a characteristic tilting and cotilting module. If A is taken to be a Nakayama algebra, then said tilting and cotilting module is a characteristic tilting module of a quasi-hereditary structure on the Auslander algebra. We prove that the self-injective Nakayama algebras are the only algebras with this property. (C) 2017 Elsevier Inc. All rights reserved.
Stichworte
Auslander algebra; Submodule categories; Quasi-hereditary algebras; Nakayama algebras; Recollement
Erscheinungsjahr
2017
Zeitschriftentitel
JOURNAL OF ALGEBRA
Band
486
Seite(n)
98-118
ISSN
0021-8693
eISSN
1090-266X
Page URI
https://pub.uni-bielefeld.de/record/2913146

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Eiriksson Ö. From submodule categories to the stable Auslander algebra. JOURNAL OF ALGEBRA. 2017;486:98-118.
Eiriksson, Ö. (2017). From submodule categories to the stable Auslander algebra. JOURNAL OF ALGEBRA, 486, 98-118. doi:10.1016/j.jalgebra.2017.05.012
Eiriksson, Ö. (2017). From submodule categories to the stable Auslander algebra. JOURNAL OF ALGEBRA 486, 98-118.
Eiriksson, Ö., 2017. From submodule categories to the stable Auslander algebra. JOURNAL OF ALGEBRA, 486, p 98-118.
Ö. Eiriksson, “From submodule categories to the stable Auslander algebra”, JOURNAL OF ALGEBRA, vol. 486, 2017, pp. 98-118.
Eiriksson, Ö.: From submodule categories to the stable Auslander algebra. JOURNAL OF ALGEBRA. 486, 98-118 (2017).
Eiriksson, Ögmundur. “From submodule categories to the stable Auslander algebra”. JOURNAL OF ALGEBRA 486 (2017): 98-118.

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