Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Classification Theorem for Nuclear Purely Infinite Simple C*-Algebras   Starting from Kirchberg's theorems announced in 1994, namely O_2 tensor A is
isomorphic to O_2 for separable unital nuclear simple A and O_infinity tensor A
is isomorphic to A if in addition A is purely infinite, we prove that
KK-equivalence implies isomorphism for nonunital separable nuclear purely
infinite simple C*-algebras. It follows that if A and B are unital separable
nuclear purely infinite simple C*-algebras which satisfy the Universal
Coefficient Theorem, and if there is a graded isomorphism from K_* (A) to K_*
(B) which preserves the class of the identity, then A is isomorphic to B.
  Our main technical results are, we believe, of independent interest. We say
that two asymptotic morphisms t ---> \phi_t and t ---> \psi_t from A to B are
asymptotically unitarily equivalent if there exists a continuous unitary path t
---> u_t in the unitization B^+ such that || u_t \phi_t (a) u_t^* - \psi_t (a)
|| ---> 0 for all a in A. Let A be separable, nuclear, unital, and simple, and
let D be unital. We prove that any asymptotic morphism from A to K tensor
O_infinity tensor D is asymptotically unitarily equivalent to a homomorphism,
and two homotopic homomorphisms from A to K tensor O_infinity tensor D are
asymptotically unitarily equivalent.

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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph