On Algebras of Finite General Representation Type

Abstract

We introduce the notion of “finite general representation type” for a finite-dimensional algebra, a property related to the “dense orbit property” introduced by Chindris-Kinser-Weyman. We use an interplay of geometric, combinatorial, and algebraic methods to produce a family of algebras of wild representation type but finite general representation type. For completeness, we also give a short proof that the only local algebras of discrete general representation type are already of finite representation type. We end with a Brauer-Thrall style conjecture for general representations of algebras.