Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of real rank zero, purely infinite C*-algebras with at
  most four primitive ideals   Counterexamples to classification of purely infinite, nuclear, separable
C*-algebras (in the ideal-related bootstrap class) and with primitive ideal
space X using ideal-related K-theory occur for infinitely many finite primitive
ideal spaces X, the smallest of which having four points. Ideal-related
K-theory is known to be strongly complete for such C*-algebras if they have
real rank zero and X has at most four points for all but two exceptional
spaces: the pseudo-circle and the diamond space. In this article, we close
these two remaining cases. We show that ideal-related K-theory is strongly
complete for real rank zero, purely infinite, nuclear, separable C*-algebras
that have the pseudo-circle as primitive ideal space. In the opposite
direction, we construct a Cuntz-Krieger algebra with the diamond space as its
primitive ideal space for which an automorphism on ideal-related K-theory does
not lift.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an