Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Purely infinite simple reduced C*-algebras of one-relator separated
  graphs   Given a separated graph $(E,C)$, there are two different C*-algebras
associated to it, the full graph C*-algebra $C^*(E,C)$, and the reduced one
$C^*_{\text{red}} (E,C)$. For a large class of separated graphs $(E,C)$, we
prove that $C^*_{\text{red}} (E,C)$ either is purely infinite simple or admits
a faithful tracial state. The main tool we use to show pure infiniteness of
reduced graph C*-algebras is a generalization to the amalgamated case of a
result on purely infinite simple free products due to Dykema.

6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
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
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph