Geometric classification of simple graph algebras
  Inspired by Franks' classification of irreducible shifts of finite type we provide a short list of allowed moves on graphs that preserves the stable isomorphism class of the associated C*-algebras. We show that if two graphs have stably isomorphic and simple unital algebras then we can use these moves to transform one into the other. 
Adam P. W. S{\o}rensen
math.OA math.DS