Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplicity criterion for $C^*$-algebras associated with topological
  group quivers   Topological quivers generalize the notion of directed graphs in which the
sets of vertices and edges are locally compact (second countable) Hausdorff
spaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, and
in turn, a Cuntz-Pimsner algebra $C^*(Q).$ Given $\Gamma$ a locally compact
group and $\alpha$ and $\beta$ endomorphisms on $\Gamma,$ one may construct a
topological quiver $Q_{\alpha,\beta}(\Gamma)$ with vertex set $\Gamma,$ and
edge set $\Omega_{\alpha,\beta}(\Gamma)= \{(x,y)\in\Gamma\times\Gamma\|
\alpha(y)=\beta(x)\}.$ In \cite{Mc1}, the author examined the Cuntz-Pimsner
algebra $\cal{O}_{\alpha,\beta}(\Gamma):=C^*(Q_{\alpha,\beta}(\Gamma))$ and
found generators (and their relations) of $\cal{O}_{\alpha,\beta}(\Gamma).$ In
this paper, the author translates a known criterion for simplicity of
topological quivers into a precise criterion for the simplicity of topological
group relations.

1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio