Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-26T08:14:07.602Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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