Geodesic
The Structure of Stable Components
Canadian journal of mathematics, Tome 43 (1991) no. 3, pp. 652-672

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be an artin algebra. Let ( be a component of the stable Auslander- Reiten quiver of A. If is periodic, then the structure of G is known. Here, we are going to consider the case when is non-periodic: we will show that is isomorphic to Z with a valued quiver. In particular, there is no cyclic path in . 
Zhang, Yingbo; Lang, T. The Structure of Stable Components. Canadian journal of mathematics, Tome 43 (1991) no. 3, pp. 652-672. doi: 10.4153/CJM-1991-038-1
@article{10_4153_CJM_1991_038_1,
     author = {Zhang, Yingbo and Lang, T.},
     title = {The {Structure} of {Stable} {Components}},
     journal = {Canadian journal of mathematics},
     pages = {652--672},
     year = {1991},
     volume = {43},
     number = {3},
     doi = {10.4153/CJM-1991-038-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-038-1/}
}
TY  - JOUR
AU  - Zhang, Yingbo
AU  - Lang, T.
TI  - The Structure of Stable Components
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 652
EP  - 672
VL  - 43
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-038-1/
DO  - 10.4153/CJM-1991-038-1
ID  - 10_4153_CJM_1991_038_1
ER  - 
%0 Journal Article
%A Zhang, Yingbo
%A Lang, T.
%T The Structure of Stable Components
%J Canadian journal of mathematics
%D 1991
%P 652-672
%V 43
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-038-1/
%R 10.4153/CJM-1991-038-1
%F 10_4153_CJM_1991_038_1

[A] Auslander, M., Applications of morphisms determined by objects. Proc. Conf. on Representation Theory. Philadelphia (1976), Marcel Dekker (1978), 245–327. Google Scholar

[B] Berge, C., Graphs and hypergraphs. North-Holland Publishing Company, 1973. Google Scholar

[BG] Bongartz, K. and Gabriel, P., Covering spaces in representation theory, Invent. Math. 65(1982), 331–378. Google Scholar

[BS] Bautista, R. and Smal, S.O.ø, Nonexistent cycles, Comm. Alg. 11(1983), 1755–1767. Google Scholar

[BR] R, M.C.. Butler and Ringel, C.M., AR-sequences with few middle terms and applications to string algebras,, Comm. Alg. 15(1987), 145–179. Google Scholar

[D] Dicks, W., Groups, trees and projective modules, LNM 790(1980). Google Scholar

[GZ] Gabriel, P. and Zisman, M., Calculus of fractions and homology theory, Erg. Math. 35, Berlin-Heildelberg- New York, Springer, 1967. Google Scholar

[HPR1 Happel, D., Preiser, U. and Ringel, C.M., Vinberg's characterization of Dynkin diagrams using subadditive function with application to DTr-periodic modules, LNM 832(1979), 280–294. Google Scholar

[Re] Reidemeister, K., Einfuhrung in die kombinatorische Topologie. Reprint, Chelsea Publishing Company, New York, N.Y., 1950. Google Scholar

[Ri] Riedtmann, Chr., Algebren, Darstellungsköcher,Überlagerungen und zuriick, Comm. Math. Helv. 55 (1980), 199–224. Google Scholar

[R] Ringel, C.M., Tame algebras and integral quadratic forms, . Springer LNM 1099(1984). Google Scholar

[S] Spanier, E.H., Algebraic Topology. McGraw Hill Book Company, 1966. Google Scholar

Cité par Sources :