On the inclusion $\cO_2 \subset \cQ_2$

Jacopo Bassi; Roberto Conti

On the inclusion $\cO_2 \subset \cQ_2$

Operator Algebras 2025-05-23 v1

Authors: Jacopo Bassi , Roberto Conti

Abstract

The diadic $C^*$ -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 $C^*$ -irreducible and rigid. It follows that the injective envelopes of these two $C^*$ -algebras are $*$ -isomorphic.

Keywords

cuntz semigroup c*-algebras graph algebras

Cite

@article{arxiv.2505.16759,
  title  = {On the inclusion $\cO_2 \subset \cQ_2$},
  author = {Jacopo Bassi and Roberto Conti},
  journal= {arXiv preprint arXiv:2505.16759},
  year   = {2025}
}

Comments

Accepted for publication in Kyoto J. Math

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