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C *-algebras of extensions of groupoids by group bundles

Abstract : Given a normal subgroup bundle A of the isotropy bundle of a groupoid Σ, we obtain a twisted action of the quotient groupoid Σ/A on the bundle of group C *-algebras determined by A whose twisted crossed product recovers the groupoid C *-algebra C * (Σ). Restricting to the case where A is abelian, we describe C * (Σ) as the C *-algebra associated to a T-groupoid over the tranformation groupoid obtained from the canonical action of Σ/A on the Pontryagin dual space of A. We give some illustrative examples of this result.
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https://hal.archives-ouvertes.fr/hal-03116987
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Submitted on : Wednesday, January 20, 2021 - 5:38:46 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM
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Marius Ionescu, Alex Kumjian, Jean Renault, Aidan Sims, Dana Williams. C *-algebras of extensions of groupoids by group bundles. Journal of Functional Analysis, Elsevier, In press, 280 (5), pp.108892. ⟨10.1016/j.jfa.2020.108892⟩. ⟨hal-03116987⟩

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