Identifying C*-algebras as AF - examples using categories of paths (in person)

The approximately finite dimensional (AF) algebras have a deceptively simple description - they are the "locally finite dimensional" C*-algebras. However it can be difficult to identify which C*-algebras are AF. This problem has been solved for graph algebras, but is still unsolved for higher rank graph algebras. In this talk I will give examples of categories of paths whose C*-algebras we are able to identify as the continued fraction AF algebras of Effros and Shen. These are nonstandard presentations of AF algebras, as they arise as C*-algebras of non AF groupoids. The proof relies on the recent classification results for simple nuclear C*-algebras. This is joint work with Ian Mitscher.