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arXiv · 2308.10768

Isotropy fibers of ideals in groupoid C$^{*}$-algebras

Johannes Christensen·Sergey Neshveyev
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Abstract

Given a locally compact \'etale groupoid and an ideal $I$ in its groupoid C$^*$-algebra, we show that $I$ defines a family of ideals in group C$^*$-algebras of the isotropy groups and then study to which extent $I$ is determined by this family. As an application we obtain the following results: (a) prove that every proper ideal is contained in an induced primitive ideal; (b) describe the maximal ideals; (c) classify the primitive ideals for a class of graded groupoids with essentially central isotropy.

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BibTeXRIS

Johannes Christensen, Sergey Neshveyev. 2023-08-21. Isotropy fibers of ideals in groupoid C$^{*}$-algebras. https://doi.org/10.1016/j.aim.2024.109696

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