Abstract
A complete description is provided for the unitary normalizer of the diagonal Cartan subalgebra D2 in the 2-adic ring C⁎-algebra Q2, which generalizes and unifies analogous results for Cuntz and Bunce-Deddens algebras. Furthermore, the inclusion O2⊂Q2 is proved not to be regular. Finally, countably many novel permutative endomorphisms of Q2 are exhibited with prescribed images of the generator U.
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