Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On simple labelled graph $C^*$-algebras   We consider the simplicity of the $C^*$-algebra associated to a labelled
space $(E,\CL,\bE)$, where $(E,\CL)$ is a labelled graph and $\bE$ is the
smallest accommodating set containing all generalized vertices. We prove that
if $C^*(E, \CL, \bE)$ is simple, then $(E, \CL, \bE)$ is strongly cofinal, and
if, in addition, $\{v\}\in \bE$ for every vertex $v$, then $(E, \CL, \bE)$ is
disagreeable. It is observed that $C^*(E, \CL, \bE)$ is simple whenever $(E,
\CL, \bE)$ is strongly cofinal and disagreeable, which is recently known for
the $C^*$-algebra $C^*(E, \CL, \CEa)$ associated to a labelled space $(E, \CL,
\CEa)$ of the smallest accommodating set $\CEa$.

7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex