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

2010/02/23 by Bernt Tore Jensen, Jensen, Bernt Tore, Xiuping Su +1
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1002.4432

openalex publication_date 2010/02/23 · arxiv created 2012/07/05 · arxiv updated 2012/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \radE_kQP. Using generic equivalence, we show that the quiver Q has the property that there exists a dense open \Aut_kQ P-orbit in \radE_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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