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Comparison Properties of the Cuntz semigroup and applications to C*-algebras

  • Joan Bosa,
    School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, G12 8QW, Glasgow, UK
  • Henning Petzka,
    Fraunhofer Institute for Intelligent Analysis and Information Systems IAIS, Schloss Birlinghoven, 53757 Sankt Augustin, Germany
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Abstract

We study comparison properties in the category $\mathrm{Cu}$ aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and $\omega$-comparison. We show differences of all properties by providing examples, which suggest that the corona factorization for C*-algebras might allow for both finite and infinite projections. In addition, we show that R{\o}rdam's simple, nuclear C*-algebra with a finite and an infinite projection does not have the CFP.
Keywords: classification of C*-algebras, cuntz semigroup classification of C*-algebras, cuntz semigroup
MSC Classifications: 46L35, 06F05, 46L05, 19K14 show english descriptions Classifications of $C^*$-algebras
Ordered semigroups and monoids [See also 20Mxx]
General theory of $C^*$-algebras
$K_0$ as an ordered group, traces
46L35 - Classifications of $C^*$-algebras
06F05 - Ordered semigroups and monoids [See also 20Mxx]
46L05 - General theory of $C^*$-algebras
19K14 - $K_0$ as an ordered group, traces
 

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