Abstract.
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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: January 31, 1997
Rights and permissions
About this article
Cite this article
Zwara, G. Degenerations for representations of extended Dynkin quivers. Comment. Math. Helv. 73, 71–88 (1998). https://doi.org/10.1007/s000140050046
Issue Date:
DOI: https://doi.org/10.1007/s000140050046