Algebraic singular functions are not always dense in the C*-singular ideal

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• Nora Szakacs (University of Manchester)
• Thursday 17 July 2025, 15:05-15:45
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TGAW02 - C*-algebras: classification and dynamical constructions

For Hausdorff ample groupoids, both the complex Steinberg algebra and the reduced C-algebra are simple if the groupoid is minimal and effective. In the non-Hausdorff case, there is a maximal ideal that might crop up consisting of functions whose support has empty interior, called the singular ideal. It is an open question whether there are minimal and effective ample groupoids where there are no nonzero singular functions in the Steinberg algebra (which we term algebraic singular functions) but there are nonzero singular functions in the reduced C-algebra. More generally, it was not known whether algebraic singular functions are always dense in the C*-singular ideal. We present an example where the latter claim fails. Even a minimal and effective counterexample exists. This is joint work with Diego Martínez.

This talk is part of the Isaac Newton Institute Seminar Series series.

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