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Degenerations of Finite-Dimensional Modules are Given by Extensions

Published online by Cambridge University Press:  04 December 2007

Grzegorz Zwara
Grzegorz Zwara
Affiliation:
Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland. E-mail: gzwara@mat.uni.torun.pl
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Abstract

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Let A be a finite-dimensional k-algebra over algebraically closed field k and $m{\rm mod}\, A$ be the category of finite-dimensional left A-modules. We show that a module M in ${\rm mod}\, A$ degenerates to another module N in ${\rm mod}\, A$ if and only if there is an exact sequence $0\to N\to M\oplus Z\to Z\to 0$ in ${\rm mod}\, A$ for some A-module Z. Moreover, we give a description of minimal degenerations of finite-dimensional A-modules.

Keywords

modulesdegenerations
Type
Research Article
Information
Compositio Mathematica , Volume 121 , Issue 2 , April 2000 , pp. 205 - 218
Copyright
© 2000 Kluwer Academic Publishers