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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Degenerations for modules
over representation-finite algebras


Author: Grzegorz Zwara
Journal: Proc. Amer. Math. Soc. 127 (1999), 1313-1322
MSC (1991): Primary 14L30, 16G60, 16G70
Published electronically: January 27, 1999
MathSciNet review: 1476404
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04714-0
PII: S 0002-9939(99)04714-0
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
Article copyright: © Copyright 1999 American Mathematical Society