Stable equivalence preserves representation type

Krause H (1997)
Commentarii Mathematici Helvetici 72(2): 266-284.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Abstract / Bemerkung
Given two finite dimensional algebras Lambda and Gamma, it is shown that Lambda is of wild representation type if and only if Gamma is of wild representation type provided that the stable categories of finite dimensional modules over Lambda and Gamma are equivalent. The proof uses generic modules. In fact, a stable equivalence induces a bijection between the isomorphism classes of generic modules over Lambda and Gamma, and the result follows from certain additional properties of this bijection. In the second part of this paper the Auslander-Reiten translation is extended to an operation on the category of all modules. It is shown that various finiteness conditions are preserved by this operation. Moreover, the Auslander-Reiten translation induces a homeomorphism between the set of non-projective and the set of non-injective points in the Ziegler spectrum. As a consequence one obtains that For an algebra of tame representation type every generic module remains fixed under the Auslander-Reiten translation.
Stichworte
generic module; stable equivalence; Ziegler spectrum; Auslander-Reiten; translation
Erscheinungsjahr
1997
Zeitschriftentitel
Commentarii Mathematici Helvetici
Band
72
Ausgabe
2
Seite(n)
266-284
ISSN
0010-2571
Page URI
https://pub.uni-bielefeld.de/record/1627425

Zitieren

Krause H. Stable equivalence preserves representation type. Commentarii Mathematici Helvetici. 1997;72(2):266-284.
Krause, H. (1997). Stable equivalence preserves representation type. Commentarii Mathematici Helvetici, 72(2), 266-284. https://doi.org/10.1007/s000140050016
Krause, H. (1997). Stable equivalence preserves representation type. Commentarii Mathematici Helvetici 72, 266-284.
Krause, H., 1997. Stable equivalence preserves representation type. Commentarii Mathematici Helvetici, 72(2), p 266-284.
H. Krause, “Stable equivalence preserves representation type”, Commentarii Mathematici Helvetici, vol. 72, 1997, pp. 266-284.
Krause, H.: Stable equivalence preserves representation type. Commentarii Mathematici Helvetici. 72, 266-284 (1997).
Krause, Henning. “Stable equivalence preserves representation type”. Commentarii Mathematici Helvetici 72.2 (1997): 266-284.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar