Representation dimension: An invariant under stable equivalence
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- by Xiangqian Guo
- Trans. Amer. Math. Soc. 357 (2005), 3255-3263
- DOI: https://doi.org/10.1090/S0002-9947-04-03596-2
- Published electronically: October 7, 2004
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Abstract:
In this paper, we prove that the representation dimension is an invariant under stable equivalence.References
- M. Auslander: Representation dimension of artin algebras, Lecture notes, Queen Mary College, London, 1971.
- Maurice Auslander, Representation theory of Artin algebras. I, II, Comm. Algebra 1 (1974), 177–268; ibid. 1 (1974), 269–310. MR 349747, DOI 10.1080/00927877408548230
- Maurice Auslander and Idun Reiten, Stable equivalence of Artin algebras, Proceedings of the Conference on Orders, Group Rings and Related Topics (Ohio State Univ., Columbus, Ohio, 1972) Lecture Notes in Math., Vol. 353, Springer, Berlin, 1973, pp. 8–71. MR 0335575
- Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. VI. A functorial approach to almost split sequences, Comm. Algebra 6 (1978), no. 3, 257–300. MR 472919, DOI 10.1080/00927877808822246
- Maurice Auslander and Idun Reiten, Stable equivalence of dualizing $R$-varieties, Advances in Math. 12 (1974), 306–366. MR 342505, DOI 10.1016/S0001-8708(74)80007-1
- Maurice Auslander and Idun Reiten, Stable equivalence of dualizing $R$-varieties. V. Artin algebras stably equivalent to hereditary algebras, Advances in Math. 17 (1975), no. 2, 167–195. MR 404243, DOI 10.1016/0001-8708(75)90091-2
- Maurice Auslander, Idun Reiten, and Sverre O. Smalø, Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, vol. 36, Cambridge University Press, Cambridge, 1995. MR 1314422, DOI 10.1017/CBO9780511623608
- Osamu Iyama, Finiteness of representation dimension, Proc. Amer. Math. Soc. 131 (2003), no. 4, 1011–1014. MR 1948089, DOI 10.1090/S0002-9939-02-06616-9
- Roberto Martínez-Villa, Algebras stably equivalent to $l$-hereditary, Representation theory, II (Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., 1979) Lecture Notes in Math., vol. 832, Springer, Berlin, 1980, pp. 396–431. MR 607166
Bibliographic Information
- Xiangqian Guo
- Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, People’s Republic of China
- Address at time of publication: Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
- Email: guoxq007@hotmail.com
- Received by editor(s): August 24, 2003
- Received by editor(s) in revised form: November 20, 2003
- Published electronically: October 7, 2004
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 357 (2005), 3255-3263
- MSC (2000): Primary 16G10
- DOI: https://doi.org/10.1090/S0002-9947-04-03596-2
- MathSciNet review: 2135745
Dedicated: Dedicated To Daidai Cha