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-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-central sequence algebra.

Keywords
projective $C^*$-algebras, RFD $C^*$-algebras, almost commuting matrices, tracial ultraproducts, order zero maps
Mathematical Subject Classification 2010
Primary: 46L05
Milestones
Received: 13 September 2017
Accepted: 11 January 2019
Published: 24 October 2019
Authors
Don Hadwin
Department of Mathematics and Statistics
University of New Hampshire
Durham
United States
Tatiana Shulman
Institute of Mathematics
Polish Academy of Sciences
Warsaw
Poland