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

Bernt Tore Jensen, Xiuping Su

Research output: Contribution to journalArticle

1 Citation (Scopus)
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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 languageEnglish
Pages (from-to)1095-1136
Number of pages42
JournalAlgebras and Representation Theory
Volume17
Issue number4
Early online date20 Jul 2013
DOIs
Publication statusPublished - 1 Aug 2014

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Quiver
Endomorphisms
Automorphism Group
Equivalence
Projective Representation
Complex number
Orbit
If and only if
Cycle

Keywords

  • Adjoint action
  • Automorphism groups
  • Generic equivalence
  • Quivers

Cite this

Adjoint action of automorphism groups on radical endomorphisms, generic equivalence and Dynkin quivers. / Jensen, Bernt Tore; Su, Xiuping.

In: Algebras and Representation Theory, Vol. 17, No. 4, 01.08.2014, p. 1095-1136.

Research output: Contribution to journalArticle

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