For a fixed prime , a noncommutative solenoid as defined by Frederic Latremoliere and Judith PackerĀ is a twisted group C*-algebra , where is an additive discrete group and is a valued group -cocycle (multiplier) on . In this talk, we first review the classification of all NC solenoids in terms of their defining multipliers using theory. From there, we discuss two constructions for projective modules over the irrational NC solenoids and how they are related: one by constructing the Heisenberg equivalence bimodule of Rieffel utilizing the adic numbers, and the other by writing the NC solenoids as direct limits of noncommutative tori.
Noncommutative solenoids and their finitely generated projective modules