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C¿-algebras of extensions of groupoids by group bundles

Journal Article


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.

Publication Date


  • 2021

Citation


  • Ionescu, M., Kumjian, A., Renault, J. N., Sims, A., & Williams, D. P. (2021). C¿-algebras of extensions of groupoids by group bundles. Journal of Functional Analysis, 280(5). doi:10.1016/j.jfa.2020.108892

Scopus Eid


  • 2-s2.0-85097742415

Web Of Science Accession Number


Volume


  • 280

Issue


  • 5

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.

Publication Date


  • 2021

Citation


  • Ionescu, M., Kumjian, A., Renault, J. N., Sims, A., & Williams, D. P. (2021). C¿-algebras of extensions of groupoids by group bundles. Journal of Functional Analysis, 280(5). doi:10.1016/j.jfa.2020.108892

Scopus Eid


  • 2-s2.0-85097742415

Web Of Science Accession Number


Volume


  • 280

Issue


  • 5