Variations of projectivity for C*-algebras

TL;DR

This paper investigates different forms of projectivity in C*-algebras, focusing on lifting problems, and demonstrates that commuting families of order zero maps can be lifted from von Neumann algebras to C*-algebras.

Contribution

It introduces new lifting results for order zero maps in the context of C*-algebras, expanding understanding of their structural properties.

Findings

Commuting families of order zero maps can be lifted from von Neumann to C*-central sequence algebras.

Established conditions under which lifting problems for C*-algebras have solutions.

Enhanced the theory of projectivity and lifting in operator algebras.

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.