Algebras of amenable representation type

Contact: Christian Kaiser (kaiser@mpim-bonn.mpg.de)

In representation theory of algebras, one measures the complexity of the category of finitely generated modules by representation type. While a complete classification of indecomposables is possible for finite and tame type, this problem is considered hopeless in the wild case.
Recently, G. Elek has introduced the notion of amenable representation type and conjectured its equivalence to tameness: instead of checking if the indecomposable modules in every dimension occur in a finite number of one-parameter families, one should check whether every indecomposable module is “almost” the direct sum of modules of bounded dimension.
In this talk, we will discuss the definition and motivate the conjecture by studying examples of amenable and non-amenable algebras and consider strategies to prove the conjecture for known classes of algebras.