The existence of bounded infinite $D$Tr-orbits
HTML articles powered by AMS MathViewer
- by Shi Ping Liu and Rainer Schulz PDF
- Proc. Amer. Math. Soc. 122 (1994), 1003-1005 Request permission
Abstract:
We construct an indecomposable module over a symmetric algebra whose DTr-ovbil is infinite and bounded. This yields a counterexample to a conjecture which states that the number of modules in an Auslander-Reiten component having the same length is finite.References
- Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. III. Almost split sequences, Comm. Algebra 3 (1975), 239–294. MR 379599, DOI 10.1080/00927877508822046
- Dagmar Baer, Noetherian categories and representation theory of hereditary Artin algebras, Comm. Algebra 13 (1985), no. 1, 247–258. MR 768095, DOI 10.1080/00927878508823157
- Raymundo Bautista and Flávio Ulhoa Coelho, On the existence of modules which are neither preprojectives nor preinjectives, J. Algebra 168 (1994), no. 2, 430–442. MR 1292773, DOI 10.1006/jabr.1994.1237
- W. W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc. (3) 56 (1988), no. 3, 451–483. MR 931510, DOI 10.1112/plms/s3-56.3.451
- Vesselin N. Gasharov and Irena V. Peeva, Boundedness versus periodicity over commutative local rings, Trans. Amer. Math. Soc. 320 (1990), no. 2, 569–580. MR 967311, DOI 10.1090/S0002-9947-1990-0967311-0
- Shi Ping Liu, Degrees of irreducible maps and the shapes of Auslander-Reiten quivers, J. London Math. Soc. (2) 45 (1992), no. 1, 32–54. MR 1157550, DOI 10.1112/jlms/s2-45.1.32
- Eugenia Marmolejo and Claus Michael Ringel, Modules of bounded length in Auslander-Reiten components, Arch. Math. (Basel) 50 (1988), no. 2, 128–133. MR 930114, DOI 10.1007/BF01194570
- Claus Michael Ringel, Representation theory of finite-dimensional algebras, Representations of algebras (Durham, 1985) London Math. Soc. Lecture Note Ser., vol. 116, Cambridge Univ. Press, Cambridge, 1986, pp. 7–79. MR 897319
- Rainer Schulz, Boundedness and periodicity of modules over QF rings, J. Algebra 101 (1986), no. 2, 450–469. MR 847170, DOI 10.1016/0021-8693(86)90204-8
- Ying Bo Zhang, The modules in any component of the AR-quiver of a wild hereditary Artin algebra are uniquely determined by their composition factors, Arch. Math. (Basel) 53 (1989), no. 3, 250–251. MR 1006714, DOI 10.1007/BF01277058
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 1003-1005
- MSC: Primary 16G10; Secondary 16G70
- DOI: https://doi.org/10.1090/S0002-9939-1994-1223516-4
- MathSciNet review: 1223516