Classification of non-simple purely infinite C*-algebras

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Certain classes of C*-algebras may be classified by simple invariants. This is well-known for purely infinite, nuclear, separable, simple C*-algebras. Allowing non-simple C*-algebras adds a new topological complexity to the classification problem, which is not yet understood in general. In many case, a newly found invariant gives complete classification results. In particular, this new invariant gives a strong classification theorem for graph C*-algebras and for C*-algebras over finite spaces whose Hasse diagram is a quiver. This project will further develop this approach to classification of non-simple C*-algebras.In particular, we want to find out which values the invariant may take on graph C*-algebras, how and with what data to compute the invariant explicitly, and how to extend the classification result to other classes of examples. For graph C*-algebras, we want to implement a computer algorithm that decides whether two graph C*-algebras are isomorphic using the invariant. The invariant also hints at how to enlarge the class of graph C*-algebras without losing too much of their nice structure. These hints shall be followed to find more general models for classifiable purely infinite C*-algebras.