Charakterisierung von Groupoid C*-Algebren von Nicht-Hausdorff Étale Groupoids (Vortrag
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Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C -algebras containing a commutative C -algebra. However, there are many natural settings in which the Kumjian–Renault theory does not apply, in part because the groupoids which arise are not Hausdorff.
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