Document Type

Article

Publication Date

2018

Publication Title

New York Journal of Mathematics

ISSN

1076-9803

Volume

24a

First Page

155

Last Page

191

Abstract

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.

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