{"paper":{"title":"Adjoint action of automorphism groups on radical endomorphisms, generic equivalence and Dynkin quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bernt Tore Jensen, Xiuping Su","submitted_at":"2010-02-23T22:44:43Z","abstract_excerpt":"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 $\\radE_{kQ}P$. Using generic equivalence, we show that the quiver $Q$ has the property that there exists a dense open $\\Aut_{kQ} P$-orbit in $\\radE_{kQ} P$, for all projective representations $P$, if and only if $Q$ is a Dynkin quiver. This gives a new characterisation of Dynkin quivers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4432","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}