Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative Solenoids   A noncommutative solenoid is the C*-algebra $C^\ast(\Q_N^2,\sigma)$ where
$\Q_N$ is the group of the $N$-adic rationals twisted and $\sigma$ 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.

28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th