Commentarii Mathematici Helvetici


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Volume 73, Issue 1, 1998, pp. 71–88
DOI: 10.1007/s000140050046

Published online: 1998-03-31

Degenerations for representations of extended Dynkin quivers

Grzegorz Zwara[1]

(1) Nicolaus Copernicus University, Torun, Poland

Let A be the path algebra of a quiver of extended Dynkin type $ \tilde {\Bbb {A}}_n, \tilde {\Bbb {D}}_n, \tilde {\Bbb {E}}_6, \tilde {\Bbb {E}}_7 $ or $ \tilde {\Bbb {E}}_8 $. We show that a finite dimensional A-module M degenerates to another A-module N if and only if there are short exact sequences $ 0 \to U_i \to M_i \to V_i \to 0 $ of A-modules such that $ M = M_1 $, $ M_{i+1} = U_i \oplus V_i $ for $ 1 \leq i \leq s $ and $ N = M_{s+1} $ are true for some natural number s.

Keywords: Modules, degenerations, extended Dynkin diagrams

Zwara Grzegorz: Degenerations for representations of extended Dynkin quivers. Comment. Math. Helv. 73 (1998), 71-88. doi: 10.1007/s000140050046