On quasidiagonal $C^*$-algebras

Abstract

We give a detailed survey of the theory of quasidiagonal $C^*$-algebras. The main structural results are presented and various functorial questions around quasidiagonality are discussed. In particular we look at what is currently known (and not known) about tensor products, quotients, extensions, free products, etc. of quasidiagonal $C^*$-algebras. We also point out how quasidiagonality is connected to some important open problems.