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Degenerations for modules over representation-finite algebras

Authors:	Grzegorz Zwara

Institution:	Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Torun, Poland

Abstract:	Let be a representation-finite algebra. We show that a finite dimensional -module degenerates to another -module if and only if the inequalities $\dim _{K} Hom_{A}(M,X)\leq \dim _{K} Hom_{A}(N,X)$ hold for all -modules . We prove also that if $\operatorname{Ext}_{A}^{1}(X,X)=0$ for any indecomposable -module , then any degeneration of -modules is given by a chain of short exact sequences.

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