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DEFORMATION OF FELL BUNDLES
Published online by Cambridge University Press: 31 October 2025
Abstract
In this paper we study deformations of 
$C^*$-algebras that are given as cross-sectional 
$C^*$-algebras of Fell bundles 
$\mathcal A$ over locally compact groups G. Our deformation comes from a direct deformation of the Fell bundles 
$\mathcal A$ via certain parameters, such as automorphisms of the Fell bundle, group cocycles, or central group extensions of G by the circle group 
$\mathbb T$, and then taking cross-sectional algebras of the deformed Fell bundles. We then show that this direct deformation method is equivalent to the deformation via the dual coactions by similar parameters as studied previously in [4, 7].
MSC classification
Secondary:
22D35: Duality theorems
Information
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc
Footnotes
This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Project-ID 427320536 SFB 1442 and under Germany’s Excellence Strategy EXC 2044 390685587, Mathematics Münster: Dynamics, Geometry, Structure; and by CNPq/CAPES/Humboldt – Brazil.
Communicated by Dana P. Williams
Dedicated to the memory of Iain Raeburn (1949–2023)
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