A look at the inner structure of the 2-adic ring C*-algebra and its automorphism groups
We undertake a systematic study of the so-called 2-adic ring C-algebra Q2. This is the
universal C-algebra generated by a unitary U and an isometry S2 such that S2U = U2S2
and S2S
2+US2S
2U = 1. Notably, it contains a copy of the Cuntz algebra O2 = C(S1;S2)
through the injective homomorphism mapping S1 to US2. Among the main results, the
relative commutant C(S2) 9 Q2 is shown to be trivial. This in turn leads to a rigidity
property enjoyed by the inclusion O2 ` Q2, namely the endomorphisms of Q2 that restrict