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The existence of bounded infinite $ D$Tr-orbits

Authors: Shi Ping Liu and Rainer Schulz
Journal: Proc. Amer. Math. Soc. 122 (1994), 1003-1005
MSC: Primary 16G10; Secondary 16G70
MathSciNet review: 1223516
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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.

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  • [1] M. Auslander and I. Reiten, Representation theory of Artin algebras III: Almost split sequences, Comm. Algebra 3 (1975), 239-294. MR 0379599 (52:504)
  • [2] D. Baer, Noetherian categories and representation theory of hereditary Artin algebras, Comm. Algebra 13 (1984), 247-258. MR 768095 (86i:16033)
  • [3] R. Bautista and F. U. Coelho, On the existence of modules which are neither preprojective nor preinjective, J. Algebra (to appear). MR 1292773 (95m:16007)
  • [4] W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc. (3) 56 (1988), 451-483. MR 931510 (89c:16028)
  • [5] V. N. Gasharov and I. V. Peeva, Boundedness versus periodicity over commutative local rings, Trans. Amer. Math. Soc. 320 (1990), 569-580. MR 967311 (90k:13011)
  • [6] S. Liu, Degrees of irreducible maps and the shapes of Auslander-Reiten quivers, J. London Math. Soc. (2) 45 (1992), 32-54. MR 1157550 (93f:16015)
  • [7] E. Marmolejo and C. M. Ringel, Modules of bounded length in Auslander-Reiten components, Arch. Math. 50 (1988), 128-133. MR 930114 (89f:16042)
  • [8] C. M. Ringel, Representation theory of finite dimensional algebras, London Math. Soc. Lecture Notes Ser., vol. 116, Cambridge Univ. Press, Cambridge, 1986, pp. 7-79. MR 897319 (89c:16030)
  • [9] R. Schulz, Boundedness and periodicity of modules over QF rings, J. Algebra 101 (1986), 450-469. MR 847170 (87i:16023)
  • [10] Y. 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. 53 (1989), 250-251. MR 1006714 (90f:16029)

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Keywords: Artin algebra, Auslander-Reiten quiver, DTr-orbit
Article copyright: © Copyright 1994 American Mathematical Society

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