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.
|Number of pages||42|
|Journal||Algebras and Representation Theory|
|Early online date||20 Jul 2013|
|Publication status||Published - 1 Aug 2014|
- Adjoint action
- Automorphism groups
- Generic equivalence
FingerprintDive into the research topics of 'Adjoint action of automorphism groups on radical endomorphisms, generic equivalence and Dynkin quivers'. Together they form a unique fingerprint.
- Department of Mathematical Sciences - Senior Lecturer
Person: Research & Teaching