Structure and K-theory of crossed products by proper actions

Echterhoff, Siegfried; Emerson, Heath

doi:10.1016/j.exmath.2011.05.001

Cited by 33 publications

(42 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. From [24], we know that the C 0 (G/K) ⋊ G-module p · (C 0 (G/K) ⋊ G) and the C * r (K)module C correspond under Morita equivalence. In fact, C c (G) can be regarded as a right C c (K)-module and a left C c (G, C c (G/K))-module.…”

Section: Definition 38 ([44]) the Higher Index Map Indexmentioning

confidence: 99%

See 1 more Smart Citation

Positive scalar curvature and Poincaré duality for proper actions

Guo

Mathai

Wang

2019

J. Noncommut. Geom.

View full text Add to dashboard Cite

For G an almost-connected Lie group, we study G-equivariant index theory for proper co-compact actions with various applications, including obstructions to and existence of G-invariant Riemannian metrics of positive scalar curvature. We prove a rigidity result for almost-complex manifolds, generalising Hattori's results, and an analogue of Petrie's conjecture. When G is an almost-connected Lie group or a discrete group, we establish Poincaré duality between G-equivariant K-homology and K-theory, observing that Poincaré duality does not necessarily hold for general G.

show abstract

Section: Definition 38 ([44]) the Higher Index Map Indexmentioning

confidence: 99%

“…where K is the space of compact operators on the Hilbert C 0 (G/K) ⋊ G-module. See details in [24,Example 5.2]. Hence, the module 1 · C * r (K) corresponds to p · (C 0 (G/K) ⋊ G) under Morita equivalence:…”

Section: Definition 38 ([44]) the Higher Index Map Indexmentioning

confidence: 99%

Positive scalar curvature and Poincaré duality for proper actions

Guo

Mathai

Wang

2019

J. Noncommut. Geom.

View full text Add to dashboard Cite

show abstract

“…In this section we examine the ramifications for the action ↵ of the various properness conditions covered in Section 2. For the state of the art in the case of proper actions, see [EE11].…”

Section: ⇤ -Ramificationsmentioning

confidence: 99%

Operator Algebras and Their Applications

Doran

Park

2016

Contemporary Mathematics

View full text Add to dashboard Cite

Abstract. Three properness conditions for actions of locally compact groups on C ⇤ -algebras are studied, as well as their dual analogues for coactions. To motivate the properness conditions for actions, the commutative cases (actions on spaces) are surveyed; here the conditions are known: proper, locally proper, and pointwise properness, although the latter property has not been so well studied in the literature. The basic theory of these properness conditions is summarized, with somewhat more attention paid to pointwise properness. C ⇤ -characterizations of the properties are proved, and applications to C ⇤ -dynamical systems are examined. This paper is partially expository, but some of the results are believed to be new.

show abstract

“…Describing this structure in a general setting is a difficult task. 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].…”

Section: Introductionmentioning

confidence: 99%

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

Kamalov¹

2017

Bulletin of the Korean Mathematical Society

View full text Add to dashboard Cite

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.

show abstract

Structure and K-theory of crossed products by proper actions

Cited by 33 publications

References 28 publications

Positive scalar curvature and Poincaré duality for proper actions

Positive scalar curvature and Poincaré duality for proper actions

Operator Algebras and Their Applications

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

Contact Info

Product

Resources

About

Structure and K-theory of crossed products by proper actions

Cited by 33 publications

References 28 publications

Positive scalar curvature and Poincaré duality for proper actions

Positive scalar curvature and Poincaré duality for proper actions

Operator Algebras and Their Applications

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

Contact Info

Product

Resources

About

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