Year: 2011
Type: preprint
Abstract: A noncommutative solenoid is the C*-algebra $C^\ast(\Q_N^2,σ)$ where $\Q_N$ is the group of the $N$-adic rationals twisted and $σ$ is a multiplier of $\Q_N^2$. In this paper, we use techniques from noncommutative topology to classify these C*-algebras up to *-isomorphism in terms of the multipliers of $\Q_N^2$. We also establish a necessary and sufficient condition for simplicity of noncommutative solenoids, compute their K-theory and show that the $K_0$ groups of noncommutative solenoids are given by the extensions of $\Z$ by $\Q_N$. 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.
Source: arXiv (Cornell University)
Authors: Latremoliere, Frederic, Packer, Judith
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3038060700