The auslander-reiten translation in submodule categories

Ringel CM, Schmidmeier M (2008)
Transactions of the American Mathematical Society 360(2): 691-716.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor*in
Ringel, Claus MichaelUniBi; Schmidmeier, Markus
Abstract / Bemerkung
Let Lambda be an artin algebra or, more generally, a locally bounded associative algebra, and S(Lambda) the category of all embeddings (A subset of B) where B is a finitely generated Lambda-module and A is a submodule of B. Then S(Lambda) is an exact Krull-Schmidt category which has Auslander-Reiten sequences. In this manuscript we show that the Auslander-Reiten translation in S(Lambda) can be computed within mod Lambda by using our construction of minimal monomorphisms. If in addition. is uniserial, then any indecomposable nonprojective object in S(Lambda) is invariant under the sixth power of the Auslander-Reiten translation.
Stichworte
auslander-Reiten sequences; triangulated categories; approximations
Erscheinungsjahr
2008
Zeitschriftentitel
Transactions of the American Mathematical Society
Band
360
Ausgabe
2
Seite(n)
691-716
ISSN
0002-9947
Page URI
https://pub.uni-bielefeld.de/record/1631243

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Ringel CM, Schmidmeier M. The auslander-reiten translation in submodule categories. Transactions of the American Mathematical Society. 2008;360(2):691-716.
Ringel, C. M., & Schmidmeier, M. (2008). The auslander-reiten translation in submodule categories. Transactions of the American Mathematical Society, 360(2), 691-716. doi:10.1090/S0002-9947-07-04183-9
Ringel, C. M., and Schmidmeier, M. (2008). The auslander-reiten translation in submodule categories. Transactions of the American Mathematical Society 360, 691-716.
Ringel, C.M., & Schmidmeier, M., 2008. The auslander-reiten translation in submodule categories. Transactions of the American Mathematical Society, 360(2), p 691-716.
C.M. Ringel and M. Schmidmeier, “The auslander-reiten translation in submodule categories”, Transactions of the American Mathematical Society, vol. 360, 2008, pp. 691-716.
Ringel, C.M., Schmidmeier, M.: The auslander-reiten translation in submodule categories. Transactions of the American Mathematical Society. 360, 691-716 (2008).
Ringel, Claus Michael, and Schmidmeier, Markus. “The auslander-reiten translation in submodule categories”. Transactions of the American Mathematical Society 360.2 (2008): 691-716.