JournalscmhVol. 73 , No. 1DOI 10.1007/s000140050046

Degenerations for representations of extended Dynkin quivers

  • Grzegorz Zwara

    Nicolaus Copernicus University, Torun, Poland
Degenerations for representations of extended Dynkin quivers cover

Abstract

Let A be the path algebra of a quiver of extended Dynkin type A~n,D~n,E~6,E~7\tilde {\Bbb {A}}_n, \tilde {\Bbb {D}}_n, \tilde {\Bbb {E}}_6, \tilde {\Bbb {E}}_7 or E~8\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 0UiMiVi00 \to U_i \to M_i \to V_i \to 0 of A-modules such that M=M1M = M_1 , Mi+1=UiViM_{i+1} = U_i \oplus V_i for 1is1 \leq i \leq s and N=Ms+1N = M_{s+1} are true for some natural number s.