Selfless Inclusions of C*-Algebras

Abstract: We introduce and study a natural notion of selflessness for inclusions of C*-probability spaces, which in particular necessitates all intermediate C*-algebras to be selfless in the sense of Robert. We identify natural sources of selfless inclusions in the realms of Z-stable and free product C*-algebras. As an application of this, we prove selflessness for a new family of C*-probability spaces outside the regime of free products and group C*-algebras. These include the reduced free unitary compact quantum groups.