Relations for Grothendieck groups of Artin algebras
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- by Maurice Auslander
- Proc. Amer. Math. Soc. 91 (1984), 336-340
- DOI: https://doi.org/10.1090/S0002-9939-1984-0744624-1
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Abstract:
M. C. R. Butler has shown that if $\Lambda$ is an artin algebra of finite representation type, then the almost split sequences generate the relations for the Grothendieck group of $\Lambda$. This paper is primarily devoted to proving the converse of Butler’s result, i.e. $\Lambda$ is of finite representation type if the almost split sequences generate the relations for the Grothendieck group of $\Lambda$.References
- Maurice Auslander and Idun Reiten, Modules determined by their composition factors, Illinois J. Math. 29 (1985), no. 2, 280–301. MR 784524
- 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
- Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. IV. Invariants given by almost split sequences, Comm. Algebra 5 (1977), no. 5, 443–518. MR 439881, DOI 10.1080/00927877708822180 D. J. Benson and R. A. Parker, The Green ring of a finite group, Aarhus University, April, 1982.
- M. C. R. Butler, Grothendieck groups and almost split sequences, Integral representations and applications (Oberwolfach, 1980) Lecture Notes in Math., vol. 882, Springer, Berlin-New York, 1981, pp. 357–368. MR 646111
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 336-340
- MSC: Primary 16A46; Secondary 16A54, 16A64, 18F30
- DOI: https://doi.org/10.1090/S0002-9939-1984-0744624-1
- MathSciNet review: 744624