Tame hereditary path algebras and amenability

Abstract

In this note we revisit the notion of amenable representation type introduced by Gábor Elek. We show that tame hereditary path algebras of quivers of extended Dynkin type over any field 𝑘 are of amenable type. This verifies a conjecture of Elek, which draws similarities to the tamewild dichotomy, for another class of tame algebras. We also show that path algebras of wild acyclic quivers over finite fields are not amenable.