Compositio Mathematica

Degenerations of Finite-Dimensional Modules are Given by Extensions

Grzegorz Zwara a1
a1 Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Torun, Poland. E-mail:

Article author query
zwara g   [Google Scholar] 


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.

Key Words: modules; degenerations.