2018/08/06 by Sebastian Eckert, Eckert, Sebastian
Mathematics · #16G20 #16G60 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1808.02092
openalex publication_date 2018/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we are concerned with the notion of amenable representation type as defined in a recent paper by Gábor Elek. Roughly speaking, an algebra is of amenable type if for all ε > 0, every finite-dimensional module has a submodule which is a direct sum of modules which are small with respect to ε such that the quotient is also small in that respect. We will show that the tame hereditary path algebras of quivers of extended Dynkin type over any field k are of amenable type, thus extending a conjecture in the aforementioned paper to another class of tame algebras. In doing so, we avoid using already known results for string algebras. We also show that path algebras of wild acyclic quivers over finite fields are not amenable.