Tame (hereditary) algebras of amenable representation type

TL;DR

This paper proves that all finite-dimensional tame hereditary algebras over any field are of amenable representation type, extending previous results and including some tilted algebras like tame concealed algebras.

Contribution

It establishes the amenability of all tame hereditary algebras and certain tilted algebras, broadening the understanding of their representation types.

Findings

All tame hereditary algebras are of amenable representation type.

The result extends to some tilted algebras, including tame concealed algebras.

The proof adapts methods from previous work on tame path algebras.

Abstract

We show that all finite dimensional, tame hereditary $k$-algebras are of amenable representation type (in the sense of G. Elek) for all fields $k$. The proof is adapted from our previous result for tame path algebras. Further, it is proven that this results extends to some tilted algebras, in particular tame concealed algebras are amenable.