On the inclusion $\cO_2 \subset \cQ_2$

Jacopo Bassi, Roberto Conti

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 f…