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SUMMARY:Algebraic singular functions are not always dense in the C*-singul
 ar ideal - Nora  Szakacs (University of Manchester)
DTSTART:20250717T140500Z
DTEND:20250717T144500Z
UID:TALK233110@talks.cam.ac.uk
DESCRIPTION:For Hausdorff ample groupoids\, both the complex Steinberg alg
 ebra 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 th
 ere are nonzero singular functions in the reduced C*-algebra. More general
 ly\, it was not known whether algebraic singular functions are always dens
 e in the C*-singular ideal. We present an example where the latter claim f
 ails. Even a minimal and effective counterexample exists. This is joint wo
 rk with Diego Mart&iacute\;nez.
LOCATION:External
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