Tensorially absorbing inclusions of C*-algebras

Abstract

Abstract When $\mathcal {D}$ is strongly self-absorbing, we say an inclusion $B \subseteq A$ of C*-algebras is $\mathcal {D}$ -stable if it is isomorphic to the inclusion $B \otimes \mathcal {D} \subseteq A \otimes \mathcal {D}$ . We give ultrapower characterizations and show that if a unital inclusion is $\mathcal {D}$ -stable, then $\mathcal {D}$ -stability can be exhibited for countably many intermediate C*-algebras concurrently. We show that such unital embeddings between unital $\mathcal {D}$ -stable C*-algebras are point-norm dense in the set of all unital embeddings, and that every unital embedding between $\mathcal {D}$ -stable C*-algebras is approximately unitarily equivalent to a $\mathcal {D}$ -stable embedding. Examples are provided.