 

Frédéric Latrémoliére
and Judith Packer
Noncommutative solenoids
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Published: 
November 7, 2018. 
Keywords: 
Twisted group C*algebras, solenoids, Nadic rationals, Nadic integers, rotation C*algebras, Ktheory,
*isomorphisms. 
Subject: 
Primary: 46L05, 46L80; Secondary: 46L35. 


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 Nadic 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 Ktheory and show that the K_{0} groups of noncommutative solenoids are given by the extensions of Z by Z[1/N]. We give a concrete description of nonsimple noncommutative solenoids as bundle of matrices over solenoid groups, and we show that irrational noncommutative solenoids are real rank zero AT C*algebras. 

Acknowledgements


Author information
Frédéric Latrémoliére:
Department of Mathematics
University of Denver
Denver, CO 80208, USA
frederic@math.du.edu
Judith Packer:
Department of Mathematics
University of Colorado
Boulder, CO 80309, USA
packer@euclid.colorado.edu

