  In this paper we associate to a qurve A (formerly known as a quasi-free or
formally smooth algebra) the one-quiver Q(A) and dimension vector a(A). This
pair contains enough information to reconstruct for all natural numbers n the
GL(n)-etale local structure of the representation scheme rep(n,A). In an
appendix we indicate how one might extend this to qurves over non-algebraically
closed fields. Further, we classify all finitely generated groups G such that
the group algebra lG is an l-qurve. If char(l)=0 these are exactly the
virtually free groups. We determine the one-quiver setting in this case and
indicate how it can be used to study the finite dimensional representations of
virtually free groups. As this approach also applies to fundamental algbras of
graphs of separable l-algebras, we state the results in this more general
setting.
