We consider various lifting problems for
-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
-central
sequence algebra.
Keywords
projective $C^*$-algebras, RFD $C^*$-algebras, almost
commuting matrices, tracial ultraproducts, order zero maps