Abstract
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 language | English |
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Pages (from-to) | 1095-1136 |
Number of pages | 42 |
Journal | Algebras and Representation Theory |
Volume | 17 |
Issue number | 4 |
Early online date | 20 Jul 2013 |
DOIs | |
Publication status | Published - 1 Aug 2014 |
Keywords
- Adjoint action
- Automorphism groups
- Generic equivalence
- Quivers