Degenerations of finite-dimensional modules are given by extensions

Authors
Citation
G. Zwara, Degenerations of finite-dimensional modules are given by extensions, COMP MATH, 121(2), 2000, pp. 205-218
Citations number
15
Categorie Soggetti
Mathematics
Journal title
COMPOSITIO MATHEMATICA
ISSN journal
0010437X → ACNP
Volume
121
Issue
2
Year of publication
2000
Pages
205 - 218
Database
ISI
SICI code
0010-437X(200004)121:2<205:DOFMAG>2.0.ZU;2-R
Abstract
Let A be a finite-dimensional k-algebra over algebraically closed field k a nd 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 i f there is an exact sequence 0 --> N --> M + Z --> Z --> 0 in mod A for som e A-module Z. Moreover, we give a description of minimal degenerations of f inite-dimensional A-modules.