Permutative representations of the 2-adic ring C*-algebra
The notion of permutative representation is generalized to the 2- adic ring C*-algebra Q2. Permutative representations of Q2 are then investigated with a particular focus on the inclusion of the Cuntz algebra O2 ⊂ Q2. Notably, every permutative representation of O2 is shown to extend automatically to a permutative representation of Q2 provided that an extension whatever exists. Moreover, all permutative extensions of a given representation of O2 are proved to be unitarily equivalent to one another.