Adjoint action of automorphism groups on radical endomorphisms, generic equivalence and Dynkin quivers

Bernt Tore Jensen, Xiuping Su

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Let Q be a connected quiver with no oriented cycles, k the field of complex numbers and P a projective representation of Q. We study the adjoint action of the automorphism group AutkQ P on the space of radical endomorphisms radEndkQ P. Using generic equivalence, we show that the quiver Q has the property that there exists a dense open Aut kQ P-orbit in radEndkQ P, for all projective representations P, if and only if Q is a Dynkin quiver. This gives a new characterisation of Dynkin quivers.

Original languageEnglish
Pages (from-to)1095-1136
Number of pages42
JournalAlgebras and Representation Theory
Issue number4
Early online date20 Jul 2013
Publication statusPublished - 1 Aug 2014



  • Adjoint action
  • Automorphism groups
  • Generic equivalence
  • Quivers

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