Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite simple labeled graph $C^*$-algebras of Cantor minimal subshifts   It is now well known that a simple graph $C^*$-algebra $C^*(E)$ of a directed
graph $E$ is either AF or purely infinite. In this paper, we address the
question of whether this is the case for labeled graph $C^*$-algebras recently
introduced by Bates and Pask as one of the generalizations of graph
$C^*$-algebras, and show that there exists a family of simple unital labeled
graph $C^*$-algebras which are neither AF nor purely infinite. Actually these
algebras are shown to be isomorphic to crossed products $C(X)\times_T \mathbb
Z$ where the dynamical systems $(X,T)$ are Cantor minimal subshifts. Then it is
an immediate consequence of well known results about this type of crossed
products that each labeled graph $C^*$-algebra in the family obtained here is
an $A\mathbb T$ algebra with real rank zero and has $\mathbb Z$ as its
$K_1$-group.

6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con