On the inclusion $\cO_2 \subset \cQ_2$

Abstract

The diadic $C^{\ast }$-algebra $\cQ_2$ contains canonically a copy of the Cuntz algebra $\cO_2$. It is shown that the inclusion $\cO_2 \subset \cQ_2$ is $C^{\ast }$-irreducible and rigid. It follows that the injective envelopes of these two $C^{\ast }$-algebras are $\ast$-isomorphic.

Accepted for publication in Kyoto J. Math