New York Journal of Mathematics
A noncommutative solenoid is a twisted group C*-algebra C*(Z[1/N]2,σ) where Z[1/N] is the group of the N-adic rationals and σ is a multiplier of Z[1/N]2. In this paper, we use techniques from noncommutative topology to classify these C*-algebras up to *-isomorphism in terms of the multipliers of Z[1/N]2. We also establish a necessary and sufficient condition for simplicity of noncommutative solenoids, compute their K-theory and show that the K0 groups of noncommutative solenoids are given by the extensions of Z by Z[1/N]. We give a concrete description of non-simple noncommutative solenoids as bundle of matrices over solenoid groups, and we show that irrational noncommutative solenoids are real rank zero AT C*-algebras.
Latrémoliére, Frédéric and Packer, Judith, "Noncommutative solenoids" (2018). Mathematics Faculty Contributions. 10.