#### Vol. 301, No. 2, 2019

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Variations of projectivity for $C^*$-algebras

### Don Hadwin and Tatiana Shulman

Vol. 301 (2019), No. 2, 421–440
DOI: 10.2140/pjm.2019.301.421
##### Abstract

We consider various lifting problems for ${C}^{\ast }$-algebras. As an application of our results we show that any commuting family of order zero maps from matrices to a von Neumann central sequence algebra can be lifted to a commuting family of order zero maps to the ${C}^{\ast }$-central sequence algebra.

##### Keywords
projective $C^*$-algebras, RFD $C^*$-algebras, almost commuting matrices, tracial ultraproducts, order zero maps
Primary: 46L05