Structure of crossed products by strictly proper actions on continuous-trace algebras

Echterhoff, Siegfried; Williams, Dana P.

doi:10.1090/s0002-9947-2014-06263-6

Cited by 5 publications

(6 citation statements)

References 28 publications

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“…, see [4] for a detailed proof, which applies mutatis mutandis by replacing S * M with S * G M and Γ with G. See also [11]. Let us recall briefly the ideas of the proof.…”

Section: And T * G M Also Has K As Minimal Isotropy Groupmentioning

confidence: 99%

Fredholm conditions for operators invariant with respect to compact Lie group actions

Baldare¹,

Côme²,

Nistor³

2021

Comptes Rendus. Mathématique

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“…, see [4] for a detailed proof, which applies mutatis mutandis by replacing S * M with S * G M and Γ with G. See also [11]. Let us recall briefly the ideas of the proof.…”

Section: And T * G M Also Has K As Minimal Isotropy Groupmentioning

confidence: 99%

Fredholm conditions for operators invariant with respect to compact Lie group actions

Baldare¹,

Côme²,

Nistor³

2021

Comptes Rendus. Mathématique

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“…, the primitive ideal spectrum of A G M , identifies with the set Ω M (E)/G. See also [9]. Explicitly, for any…”

Section: Background Materialsmentioning

confidence: 99%

Fredholm conditions for operators invariant with respect to compact Lie group actions

Baldare¹,

Côme²,

Nistor³

2020

Preprint

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Let G be a compact Lie group acting smoothly on a smooth, compact manifold M , let P ∈ ψ m (M ; E 0 , E 1 ) be a G-invariant, classical pseudodifferential operator acting between sections of two vector bundles E i → M , i = 0, 1, and let α be an irreducible representation of the group G. Then P induces a map πα(P ) : H s (M ; E 0 )α → H s−m (M ; E 1 )α between the α-isotypical components. We prove that the map πα(P ) is Fredholm if, and only if, P is transversally α-elliptic, a condition defined in terms of the principal symbol of P and the action of G on the vector bundles E i .

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“…We endow the set Γ with the same topology as in [3,Theorem 4.1]. This topology is defined in terms of convergent sequences.…”

Section: Topology On γmentioning

confidence: 99%

“…To gain any meaningful insight about A ⋊ σ G one has had to impose various conditions on A and G [1,2,4,5,7,8]. Recently Echterhoff and Williams gave a concrete description of the dual space in the case of a strictly proper action on a continuous trace C * -algebra [3]. In this paper, we investigate the topology of A ⋊ σ G when G is finite.…”

Section: Introductionmentioning

confidence: 99%

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ON THE TOPOLOGY OF THE DUAL SPACE OF CROSSED PRODUCT C^*-ALGEBRAS WITH FINITE GROUPS

Kamalov¹

2017

Bulletin of the Korean Mathematical Society

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Abstract. In this note we extend our previous result about the structure of the dual of a crossed product C * -algebra A ⋊σ G, when G is a finite group. We consider the space Γ which consists of pairs of irreducible representations of A and irreducible projective representations of subgroups of G. Our goal is to endow Γ with a topology so that the orbit space G\ Γ is homeomorphic to the dual of A ⋊σ G. In particular, we will show that if A is Hausdorff then G\ Γ is homeomorphic to A ⋊σ G.

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Structure of crossed products by strictly proper actions on continuous-trace algebras

Cited by 5 publications

References 28 publications

Fredholm conditions for operators invariant with respect to compact Lie group actions

Fredholm conditions for operators invariant with respect to compact Lie group actions

Fredholm conditions for operators invariant with respect to compact Lie group actions

ON THE TOPOLOGY OF THE DUAL SPACE OF CROSSED PRODUCT C^*-ALGEBRAS WITH FINITE GROUPS

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Structure of crossed products by strictly proper actions on continuous-trace algebras

Cited by 5 publications

References 28 publications

Fredholm conditions for operators invariant with respect to compact Lie group actions

Fredholm conditions for operators invariant with respect to compact Lie group actions

Fredholm conditions for operators invariant with respect to compact Lie group actions

ON THE TOPOLOGY OF THE DUAL SPACE OF CROSSED PRODUCT C*-ALGEBRAS WITH FINITE GROUPS

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ON THE TOPOLOGY OF THE DUAL SPACE OF CROSSED PRODUCT C^*-ALGEBRAS WITH FINITE GROUPS