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arXiv · 1902.05773

Normalizers and permutative endomorphisms of the $2$-adic ring $C^*$-algebra

Valeriano Aiello·Roberto Conti·Stefano Rossi
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Abstract

A complete description is provided for the unitary normalizer of the diagonal Cartan subalgebra $\mathcal{D}_2$ in the $2$-adic ring $C^*$-algebra $\mathcal{Q}_2$, which generalizes and unifies analogous results for Cuntz and Bunce-Deddens algebras. Furthermore, the inclusion $\mathcal{O}_2\subset\mathcal{Q}_2$ is proved not to be regular. Finally, countably many novel permutative endomorphisms of $\mathcal{Q}_2$ are exhibited with prescribed images of the generator $U$.

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Valeriano Aiello, Roberto Conti, Stefano Rossi. 2019-02-15. Normalizers and permutative endomorphisms of the $2$-adic ring $C^*$-algebra. https://doi.org/10.1016/j.jmaa.2019.123395

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