Operator algebra seminar

Speaker: Jamie Gabe (University of Southampton)

Title: Extended K-theory for C*-algebras

Abstract: I will introduce extended K-theory, a new K-theoretic invariant for C*-algebras. The invariant is computable for large classes of crossed products by endomorphisms $B \rtimes \mathbb N$, e.g. whenever B is an AF-algebra, in which case the invariant is essentially the Pimsner-Voiculescu sequence up to a suitable equivalence relation. The invariant can be used to classify large classes of separable, nuclear, (non-simple) purely infinite C*-algebras, e.g. all purely infinite C*-algebras of real rank zero which are a crossed product of an endomorphism on an AF algebra.