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Maximality of dual coactions on sectional C*-algebras of Fell bundles and applications

Alcides Buss, Siegfried Echterhoff (2015)

Studia Mathematica

We give a simple proof of the maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles over locally compact groups. This result was only known for discrete groups or for saturated (separable) Fell bundles over locally compact groups. Our proof, which is derived as an application of the theory of universal generalised fixed-point algebras for weakly proper actions, is different from these previously known cases and works for general Fell bundles over locally compact groups....

Morita equivalence of groupoid C*-algebras arising from dynamical systems

Xiaoman Chen, Chengjun Hou (2002)

Studia Mathematica

We show that the stable C*-algebra and the related Ruelle algebra defined by I. Putnam from the irreducible Smale space associated with a topologically mixing expanding map of a compact metric space are strongly Morita equivalent to the groupoid C*-algebras defined directly from the expanding map by C. Anantharaman-Delaroche and V. Deaconu. As an application, we calculate the K⁎-group of the Ruelle algebra for a solenoid.

Morita equivalence of measured quantum groupoids. Application to deformation of measured quantum groupoids by 2-cocycles

Michel Enock (2012)

Banach Center Publications

In a recent article, Kenny De Commer investigated Morita equivalence between locally compact quantum groups, in which a measured quantum groupoid, of basis ℂ², was constructed as a linking object. Here, we generalize all these constructions and concepts to the level of measured quantum groupoids. As for locally compact quantum groups, we apply this construction to the deformation of a measured quantum groupoid by a 2-cocycle.

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