Semiprojectivity with and without a group action

  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},
Compact group actions with the Rokhlin property
  • Eusebio Gardella
  • Mathematics
    Transactions of the American Mathematical Society
  • 2018
We provide a systematic and in-depth study of compact group actions with the Rokhlin property. It is show that the Rokhlin property is generic in some cases of interest; the case of totally
Semiprojectivity and the geometry of graphs
In this thesis semiprojectivity is investigated in three different settings; for commutative C-algebras, for Real C-algebras, and for C-algebras with a group action. In the setting of commutative
The minimal exact crossed product
Given a locally compact group $G$, we study the smallest exact crossed-product functor $(A,G,\alpha)\mapsto A\rtimes_{\mathcal E} G$ on the category of $G$-$C^*$-dynamical systems. As an outcome, we
The local-triviality dimension of actions of compact quantum groups
We define the local-triviality dimension for actions of compact quantum groups on unital C*-algebras, and say that the resulting compact quantum principal bundle is locally trivial when this
Equivariant dimensions of graph C*-algebras
The primitive ideal space of Deaconu–Renault groupoid C*-algebras
The main goal of this thesis is to reproduce the article [SW16] by Sims and Williams, categorising the primitive ideal space of the class of DeaconuRenault groupoid C∗-algebras generated by
Circle actions on $\mathcal{O}_2$-absorbing $C^*$-algebras
We classify circle actions with the Rokhlin property on separable, nuclear $C^*$-algebras that absorb the Cuntz algebra $\mathcal{O}_2$ tensorially. The invariant we use is the induced action on the
Projection operators nearly orthogonal to their symmetries
Regularity of simple nuclear real C*-algebras under tracial conditions
  • P. Stacey
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 2021
Abstract The Toms–Winter conjecture is verified for those separable, unital, nuclear, infinite-dimensional real C*-algebras for which the complexification has a tracial state space with compact
Crossed products by spectrally free actions


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
  • Ja A Jeong, H. Osaka
  • 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
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