New York Journal of Mathematics
Volume 24a (2018), 155-191


Frédéric Latrémoliére and Judith Packer

Noncommutative solenoids

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Published: November 7, 2018.
Keywords: Twisted group C*-algebras, solenoids, N-adic rationals, N-adic integers, rotation C*-algebras, K-theory, *-isomorphisms.
Subject: Primary: 46L05, 46L80; Secondary: 46L35.

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.


Author information

Frédéric Latrémoliére:
Department of Mathematics
University of Denver
Denver, CO 80208, USA


Judith Packer:
Department of Mathematics
University of Colorado
Boulder, CO 80309, USA