Tame hereditary path algebras and amenability

Eckert S. Tame hereditary path algebras and amenability. Bulletin of the London Mathematical Society . 2023.In this note we revisit the notion of amenable representation type introduced by Gabor Elek. We show that tame hereditary path algebras of quivers of extended Dynkin type over any field k$k$ are of amenable type. This verifies a conjecture of Elek, which draws similarities to the tame-wild dichotomy, for another class of tame algebras. We also show that path algebras of wild acyclic quivers over finite fields are not amenable