Degenerations for modules over representation-finite algebras
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Abstract:
Let $A$ be a representation-finite algebra. We show that a finite dimensional $A$-module $M$ degenerates to another $A$-module $N$ if and only if the inequalities $\dim _{K} Hom_{A}(M,X)\leq \dim _{K} Hom_{A}(N,X)$ hold for all $A$-modules $X$. We prove also that if $\operatorname {Ext}_{A}^{1}(X,X)=0$ for any indecomposable $A$-module $X$, then any degeneration of $A$-modules is given by a chain of short exact sequences.References
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Additional Information
- Grzegorz Zwara
- Affiliation: Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
- Email: gzwara@mat.uni.torun.pl
- Received by editor(s): May 6, 1997
- Received by editor(s) in revised form: August 28, 1997
- Published electronically: January 27, 1999
- Communicated by: Ken Goodearl
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1313-1322
- MSC (1991): Primary 14L30, 16G60, 16G70
- DOI: https://doi.org/10.1090/S0002-9939-99-04714-0
- MathSciNet review: 1476404