# Semiprojectivity with and without a group action

@article{Phillips2014SemiprojectivityWA,
title={Semiprojectivity with and without a group action},
author={N. Christopher Phillips and Adam P. W. S{\o}rensen and Hannes Thiel},
journal={Journal of Functional Analysis},
year={2014},
volume={268},
pages={929-973}
}
• Published 13 March 2014
• Mathematics
• Journal of Functional Analysis
10 Citations
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## References

SHOWING 1-10 OF 34 REFERENCES
Equivariant semiprojectivity
We define equivariant semiprojectivity for C*-algebras equipped with actions of compact groups. We prove that the following examples are equivariantly semiprojective: • Arbitrary finite dimensional
Extremally rich C*-crossed products and the cancellation property
• Mathematics
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
• 1998
Abstract A unital C*-algebra A is called extremally rich if the set of quasi-invertible elements A-1 ex (A)A-1 (= A-1q) is dense in A, where ex(A) is the set of extreme points in the closed unit ball
Continuous fields ofC*-algebras coming from group cocycles and actions
Recently I have been attempting to formulate a suitable C*-algebraic framework for the subject of deformation quantization [-3, 19]. Continuous fields of C*-algebras provide one of the key elements
The generator problem for Z-stable C*-algebras
• Mathematics
• 2012
The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely,
A new method in fixed point theory
EÎ'(X, A) = Ê\T, H\X, A)) where H denotes the Tate cohomology ofir [l, Chapter 12 ] and H'(X, A) is the jth Cech cohomology group of (X, A) with arbitrary coefficients and with w action induced by
Freeness of actions of finite groups on C*-algebras
We describe some of the forms of freeness of group actions on noncommutative C*-algebras that have been used, with emphasis on actions of finite groups. We give some indications of their strengths,
Crossed products, the Mackey-Rieffel-Green machine and applications
We give an introduction into the ideal structure and representation theory of crossed products by actions of locally compact groups on C*-algebras. In particular, we discuss the Mackey-Rieffel-Green
Equivariant K: Theory and Freeness of Group Actions on C Algebras
Introduction: The commutative case.- Equivariant K-theory of C*-algebras.- to equivariant KK-theory.- Basic properties of K-freeness.- Subgroups.- Tensor products.- K-freeness, saturation, and the
Outer automorphisms and reduced crossed products of simpleC*-algebras
Every outer automorphism of a separable simpleC*-Algebra is shown to have a pure state which is mapped into an inequivalent state under this automorphism. The reduced crossed product of a