Auslander-Reiten sequences under base field extension
HTML articles powered by AMS MathViewer
- by Stanisław Kasjan
- Proc. Amer. Math. Soc. 128 (2000), 2885-2896
- DOI: https://doi.org/10.1090/S0002-9939-00-05382-X
- Published electronically: April 28, 2000
- PDF | Request permission
Abstract:
We investigate the behaviour of Auslander-Reiten sequences of modules over a finite dimensional algebra over a field $k$ under base field extension. It is proved that an Auslander-Reiten sequence splits into a direct sum of Auslander-Reiten sequences provided the extension is separable in the sense of MacLane.References
- 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
- I. N. Herstein, Noncommutative rings, The Carus Mathematical Monographs, No. 15, Mathematical Association of America; distributed by John Wiley & Sons, Inc., New York, 1968. MR 0227205
- Nathan Jacobson, Lectures in abstract algebra. Vol III: Theory of fields and Galois theory, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London-New York, 1964. MR 0172871
- Christian U. Jensen and Helmut Lenzing, Homological dimension and representation type of algebras under base field extension, Manuscripta Math. 39 (1982), no. 1, 1–13. MR 672397, DOI 10.1007/BF01312441
- Christian U. Jensen and Helmut Lenzing, Model-theoretic algebra with particular emphasis on fields, rings, modules, Algebra, Logic and Applications, vol. 2, Gordon and Breach Science Publishers, New York, 1989. MR 1057608
- Shi Ping Liu, Semi-stable components of an Auslander-Reiten quiver, J. London Math. Soc. (2) 47 (1993), no. 3, 405–416. MR 1214905, DOI 10.1112/jlms/s2-47.3.405
- Shiping Liu, Shapes of connected components of the Auslander-Reiten quivers of Artin algebras, Representation theory of algebras and related topics (Mexico City, 1994) CMS Conf. Proc., vol. 19, Amer. Math. Soc., Providence, RI, 1996, pp. 109–137. MR 1388561
- Idun Reiten and Christine Riedtmann, Skew group algebras in the representation theory of Artin algebras, J. Algebra 92 (1985), no. 1, 224–282. MR 772481, DOI 10.1016/0021-8693(85)90156-5
- Claus Michael Ringel, Tame algebras and integral quadratic forms, Lecture Notes in Mathematics, vol. 1099, Springer-Verlag, Berlin, 1984. MR 774589, DOI 10.1007/BFb0072870
- C.M. Ringel, Exceptional modules are tree modules, SFB 343 preprint 96-082, Bielefeld 1996.
- Aidan Schofield, The field of definition of a real representation of a quiver $Q$, Proc. Amer. Math. Soc. 116 (1992), no. 2, 293–295. MR 1072091, DOI 10.1090/S0002-9939-1992-1072091-4
- Daniel Simson, Linear representations of partially ordered sets and vector space categories, Algebra, Logic and Applications, vol. 4, Gordon and Breach Science Publishers, Montreux, 1992. MR 1241646
Bibliographic Information
- Stanisław Kasjan
- Affiliation: Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
- MR Author ID: 333741
- Email: skasjan@mat.uni.torun.pl
- Received by editor(s): April 20, 1998
- Received by editor(s) in revised form: December 1, 1998
- Published electronically: April 28, 2000
- Additional Notes: The author was supported by Polish KBN Grant 2 P03A 007 12
- Communicated by: Ken Goodearl
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2885-2896
- MSC (1991): Primary 16G70, 16G60
- DOI: https://doi.org/10.1090/S0002-9939-00-05382-X
- MathSciNet review: 1670379
Dedicated: Dedicated to Professor Helmut Lenzing on the occasion of his sixtieth birthday