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

Valeriano Aiello; Roberto Conti; Stefano Rossi

doi:10.1016/j.jmaa.2019.123395

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

Operator Algebras 2020-03-03 v2 Group Theory

Authors: 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 $U$ .

Keywords

c*-algebras quantum groups graded algebras

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@article{arxiv.1902.05773,
  title  = {Normalizers and permutative endomorphisms of the $2$-adic ring $C^*$-algebra},
  author = {Valeriano Aiello and Roberto Conti and Stefano Rossi},
  journal= {arXiv preprint arXiv:1902.05773},
  year   = {2020}
}

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To appear in J. Math. Anal. Appl

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

Abstract

Keywords

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