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 Aut kQ P on the space of radical endomorphisms radEnd kQ P. Using generic equivalence, we show that the quiver Q has the property that there exists a dense open Aut kQ P-orbit in radEnd kQ P, for all projective representations P, if and only if Q is a Dynkin quiver. This gives a new characterisation of Dynkin quivers.
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Jensen, B.T., Su, X. Adjoint Action of Automorphism Groups on Radical Endomorphisms, Generic Equivalence and Dynkin Quivers. Algebr Represent Theor 17, 1095–1136 (2014). https://doi.org/10.1007/s10468-013-9436-9
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DOI: https://doi.org/10.1007/s10468-013-9436-9