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Valeriano Aiello, Roberto Conti, Stefano Rossi, Diagonal automorphisms of the 2-adic ring C*-algebra, The Quarterly Journal of Mathematics, Volume 69, Issue 3, September 2018, Pages 815–833, https://doi.org/10.1093/qmath/hax064
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Abstract
The 2-adic ring C*-algebra naturally contains a copy of the Cuntz algebra and, a fortiori, also of its diagonal subalgebra with Cantor spectrum. This paper is aimed at studying the group of the automorphisms of fixing pointwise. It turns out that any such automorphism leaves globally invariant. Furthermore, the subgroup is shown to be maximal abelian in . Saying exactly what the group is amounts to understanding when an automorphism of that fixes pointwise extends to . A complete answer is given for all localized automorphisms: these will extend if and only if they are the composition of a localized inner automorphism with a gauge automorphism.