scholarly journals Continuous-trace groupoid crossed products

2003 ◽  
Vol 132 (3) ◽  
pp. 707-717 ◽  
Author(s):  
Igor Fulman ◽  
Paul S. Muhly ◽  
Dana P. Williams
Keyword(s):  
Crossed Products ◽  
Continuous Trace

scholarly journals The Dixmier-Douady class of groupoid crossed products

2004 ◽  
Vol 76 (2) ◽  
pp. 223-234 ◽  
Author(s):  
Paul S. Muhly ◽  
Dana P. Williams
Keyword(s):  
Crossed Product ◽  
Crossed Products ◽  
Continuous Trace

AbstractWe give a formula for the Dixmier-Douady class of a continuous-trace groupoid crossed product that arises from an action of a locally trivial, proper, principal groupoid on a bundle of elementary C*-algebras that satisfies Fell's condition.

scholarly journals Crossed products with continuous trace

1996 ◽  
Vol 123 (586) ◽  
pp. 0-0 ◽  
Author(s):  
Siegfried Echterhoff
Keyword(s):  
Crossed Products ◽  
Continuous Trace

scholarly journals Groupoid crossed products of continuous-trace $C^*$-algebras

2014 ◽  
Vol 72 (2) ◽  
pp. 557-576 ◽  
Author(s):  
Erik van Erp ◽  
Dana P. Williams
Keyword(s):  
Crossed Products ◽  
C Algebras ◽  
Continuous Trace

Dixmier-Douady Classes of Dynamical Systems and Crossed Products

1993 ◽  
Vol 45 (5) ◽  
pp. 1032-1066 ◽  
Author(s):  
Iain Raeburn ◽  
Dana P. Williams
Keyword(s):  
Dynamical Systems ◽  
Cohomology Group ◽  
Crossed Products ◽  
Second Main Theorem ◽  
Spectral System ◽  
Two Systems ◽  
Continuous Trace ◽  
Cech Cohomology ◽  
First Main Theorem

AbstractContinuous-trace C*-algebras A with spectrum T can be characterized as those algebras which are locally Monta equivalent to C0(T). The Dixmier-Douady class δ(A) is an element of the Čech cohomology group Ȟ3(T, ℤ) and is the obstruction to building a global equivalence from the local equivalences. Here we shall be concerned with systems (A, G, α) which are locally Monta equivalent to their spectral system (C0(T),G, τ), in which G acts on the spectrum T of A via the action induced by α. Such systems include locally unitary actions as well as N-principal systems. Our new Dixmier-Douady class δ (A, G, α) will be the obstruction to piecing the local equivalences together to form a Monta equivalence of (A, G, α) with its spectral system. Our first main theorem is that two systems (A, G, α) and (B, G, β) are Monta equivalent if and only if δ (A, G, α) = δ (B, G, β). In our second main theorem, we give a detailed formula for δ (A ⋊α G) when (A, G, α) is N-principal.

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