Operator Algebra Seminar
Speaker: James Gabe, University of Glasgow
Title: Traceless AF embeddings and unsuspended E-theory
Abstract: A major open problem in C*-algebras is whether any separable, exact, quasidiagonal C*-algebra is AF embeddable, i.e. admits an embedding into an AF-algebra. Ozawa proved that the cone and the suspension of any separable, exact C*-algebra is AF embeddable, and therefore, surprisingly, many traceless C*-algebras turn out to be AF embeddable. I show that for separable, exact, traceless C*-algebras, AF embeddability and quasidiagonality are equivalent conditions which are characterised by the primitive ideal space.
By appealing to a recent theorem of Dadarlat and Pennig, I also show that for nuclear C*-algebras the primitive ideal space characterises exactly when Connes and Higson's E-theory can be unsuspended.
Please note unusual time and place! In particular, talk starts on the hour!