On generic modules for string algebras

Ringel CM (2001)
Boletín de la Sociedad Matemática Mexicana 7(1): 85-97.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
We consider a string algebra A. In case A is domestic, and G, G ' are non-isomorphic generic modules, then G ' neither generates nor cogenerates G. On the other hand, in case A is non-domestic, we are going to construct sequences G(1), G(2), . . . of pairwise non-isomorphic generic modules such that there are monomorphisms G(t) --> G(i-1) and epimorphisms G(i+1) --> G(i), for all i. The proof of the existence of such sequences answers a question raised by Bautista. In particular, we see that any non-domestic string algebra has generic modules whose endomorphism rings have a non-zero radical. Actually, we will show that in the non-domestic case there always do exist generic modules with nilpotent endomorphisms of arbitrary large nilpotency index. Of course, in the domestic case the nilpotency index of a nilpotent endomorphism of a generic modules is bounded; in fact, it is bounded by the nilpotency index of the radical of A.
Stichworte
string modules; generic modules; tame; representation type; band modules; string algebras; domestic and non-domestic algebras
Erscheinungsjahr
2001
Zeitschriftentitel
Boletín de la Sociedad Matemática Mexicana
Band
7
Ausgabe
1
Seite(n)
85-97
ISSN
1405-213X
eISSN
2296-4495
Page URI
https://pub.uni-bielefeld.de/record/1617079

Zitieren

Ringel CM. On generic modules for string algebras. Boletín de la Sociedad Matemática Mexicana. 2001;7(1):85-97.
Ringel, C. M. (2001). On generic modules for string algebras. Boletín de la Sociedad Matemática Mexicana, 7(1), 85-97.
Ringel, C. M. (2001). On generic modules for string algebras. Boletín de la Sociedad Matemática Mexicana 7, 85-97.
Ringel, C.M., 2001. On generic modules for string algebras. Boletín de la Sociedad Matemática Mexicana, 7(1), p 85-97.
C.M. Ringel, “On generic modules for string algebras”, Boletín de la Sociedad Matemática Mexicana, vol. 7, 2001, pp. 85-97.
Ringel, C.M.: On generic modules for string algebras. Boletín de la Sociedad Matemática Mexicana. 7, 85-97 (2001).
Ringel, Claus Michael. “On generic modules for string algebras”. Boletín de la Sociedad Matemática Mexicana 7.1 (2001): 85-97.

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