Degenerations for modules over representation-finite algebras

Zwara, Grzegorz

doi:10.1090/S0002-9939-99-04714-0

Degenerations for modules over representation-finite algebras
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by Grzegorz Zwara PDF

Proc. Amer. Math. Soc. 127 (1999), 1313-1322 Request permission

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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