Mansfield's imprimitivity theorem for arbitrary closed subgroups

@inproceedings{Huef2002MansfieldsIT,
  title={Mansfield's imprimitivity theorem for arbitrary closed subgroups},
  author={Astrid an Huef and Iain Raeburn},
  year={2002}
}
Let δ be a nondegenerate coaction of G on a C*-algebra B, and let H be a closed subgroup of G. The dual action δ: H → Aut(B × δ G) is proper and saturated in the sense of Rieffel, and the generalised fixed-point algebra is the crossed product of B by the homogeneous space G/H. The resulting Morita equivalence is a version of Mansfield's imprimitivity theorem which requires neither amenability nor normality of H. 
View PDF on arXiv
13 Citations
Highly Influential Citations
2
Background Citations
7
Methods Citations
5
Results Citations
2

13 Citations

Induction in stages for crossed products of C ∗ -algebras by maximal coactions ✩

Induction in stages for C*-crossed products by maximal coactions

Let δ be a maximal coaction of a locally compact group G on a C-algebra B, and let N and H be closed normal subgroups of G with N ⊆ H . We show that the process IndG/H which uses Mansfield’s bimodule…

Proper actions, fixed-point algebras and naturality in nonabelian duality

Weakly proper group actions, Mansfield's imprimitivity and twisted Landstad duality

ALCIDES BUSS AND SIEGFRIED ECHTERHOFFAbstract. Using the theory of weakly proper actions of locally compactgroups recently developed by the authors, we give a unified proof of both re-duced and…

Full and reduced coactions of locally compact groups on C*-algebras

Fell bundles and imprimitivity theorems

Our goal in this paper and two sequels is to apply the Yamagami-Muhly- Williams equivalence theorem for Fell bundles over groupoids to recover and extend all known imprimitivity theorems involving…

FELL BUNDLES AND IMPRIMITIVITY THEOREMS: MANSFIELD’S AND FELL’S THEOREMS

Abstract In the third and latest paper in this series, we recover the imprimitivity theorems of Mansfield and Fell using our technique of Fell bundles over groupoids. Also, we apply the Rieffel…

Functoriality of Rieffel's Generalised Fixed-Point Algebras for Proper Actions

We consider two categories of C*-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and…

Proper actions which are not saturated

If a locally compact group G acts properly on a locally compact space X, then the induced action on C 0 (X) is proper in the sense of Rieffel, with generalised fixed-point algebra C 0 (G\X).…

A Symmetric Imprimitivity Theorem for Commuting Proper Actions

Abstract We prove a symmetric imprimitivity theorem for commuting proper actions of locally compact groups $H$ and $K$ on a ${{C}^{*}}$ -algebra.

17 References

Imprimitivity for C*-coactions of non-amenable groups

We give a condition on a full coaction (A, G, δ) of a (possibly) non-amenable group G and a closed normal subgroup N of G which ensures that Mansfield imprimitivity works; i.e. that A×δ[mid ]G/N is…

Induced representations of crossed products by coactions

CROSSED PRODUCTS BY DUAL COACTIONS OF GROUPS AND HOMOGENEOUS SPACES

Manseld showed how to induce representations of crossed prod- ucts of C -algebras by coactions from crossed products by quotient groups and proved an imprimitivity theorem characterising these…

FULL DUALITY FOR COACTIONS OF DISCRETE GROUPS

Using the strong relation between coactions of a discrete group $G$ on $C^*$-algebras and Fell bundles over $G$ we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete…

Induced C*-algebras and Landstad duality for twisted coactions

Suppose N is a closed normal subgroup of a locally compact group G. A coaction e: A —» M(A ® C*(N)) of N on a C*-algebra A can be inflated to a coaction S of G on A , and the crossed product A x? G…

Coverings of Directed Graphs and Crossed Products of C*-Algebras by Coactions of Homogeneous Spaces

We show that if p:F→E is a covering of directed graphs, then the Cuntz–Krieger algebra C*(F) of F can be viewed as a crossed product of C*(E) by a coaction of a homogeneous space for the fundamental…

A remark on Mansfield’s imprimitivity theorem

We show that the Morita equivalence part of Mansfield’s Imprimitivity Theory can be obtained by Green’s Imprimitivity Theorem (and duality theory). In [5], Mansfield developed a very interesting…

Applications of the Connes Spectrum to C∗-dynamical systems, III

Proper Actions of Groups on C*-Algebras

Recently I have been attempting to formulate a suitable C*-algebraic framework for the subject of deformation quantization of Poisson manifolds [1,13]. Some of the main examples which I have…

The local structure of twisted covariance algebras

The fundamental problem in investigating the unitary representation theory of a separable locally compact group G is to determine its space G ̂ of (equivalence classes of) irreducible…