Calkin algebra, Kazhdan's property (T), strongly self-absorbing C*-algebras

Abstract

The Calkin algebra is not isomorphic to the corona of the stabilization of the Cuntz algebra~${\mathcal O}_\infty$, any other Kirchberg algebra, or even the corona of the stabilization of any unital, ${\mathcal Z}$-stable ${\mathrm C}^*$-algebra. The proof relies on properties of relative commutants of separable ${\mathrm C}^*$-subalgebras.