Abstract
Let A be a finite-dimensional k-algebra over algebraically closed field k and mod A be the category of finite-dimensional left A-modules. We show that a module M in mod A degenerates to another module N in mod A if and only if there is an exact sequence \(0 \to N \to M \oplus Z \to Z \to 0\) in mod A for some A-module Z. Moreover, we give a description of minimal degenerations of finite-dimensional A-modules.
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Zwara, G. Degenerations of Finite-Dimensional Modules are Given by Extensions. Compositio Mathematica 121, 205–218 (2000). https://doi.org/10.1023/A:1001778532124
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DOI: https://doi.org/10.1023/A:1001778532124