Tensorially absorbing inclusions of C*-algebras

Sarkowicz, Pawel 

Canadian journal of mathematics, Tome 77 (2025) no. 4, pp. 1315-1346

Résumé

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.

Détail

DOI : 10.4153/S0008414X24000324

Mots-clés : C*-algebras, tensor products, inclusions, strongly self-absorbing C*-algebras