Clannish algebras are of amenable representation type

Abstract

We revisit G. Elek's notion of amenable representation type, where algebras are characterised by every indecomposable module being "almost" the direct sum of modules of bounded dimension. We give a new proof of his result that string algebras are amenable that relies on the planarity of the coefficient quivers of indecomposable string and band modules. Using this connection to graph theory, we then show that clannish algebras are also of amenable type.