Comparison Properties of the CuntzSemigroup and Applications to C* -algebras

Bosa, Joan ; Petzka, Henning

Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 26-52

Résumé

We study comparison properties in the category $\text{Cu}$ aiming to lift results to the ${{\text{C}}^{\text{*}}}$ -algebraic setting. We introduce a new comparison property and relate it to both the corona factorization property $\left( \text{CFP} \right)$ and $\omega $ -comparison. We show differences of all properties by providing examples that suggest that the corona factorization for ${{\text{C}}^{\text{*}}}$ -algebras might allow for both finite and infinite projections. In addition, we show that Rørdam's simple, nuclear ${{\text{C}}^{\text{*}}}$ -algebra with a finite and an inifnite projection does not have the $\text{CFP}$ .

Détail

DOI : 10.4153/CJM-2016-049-8

Mots-clés : 46L35, 06F05, 46L05, 19K14, classification of C*-algebras, cuntz semigroup

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