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SUMMARY:Stably finite and purely infinite crossed products - Ilija Tolich 
 (Victoria University of Wellington)
DTSTART:20250704T133000Z
DTEND:20250704T140000Z
UID:TALK233821@talks.cam.ac.uk
DESCRIPTION:The C*-algebra associated to a topological groupoid can be vie
 wed as a crossed product: by the partial action of the inverse semigroup o
 f bisections on the continuous functions on the unit space. Analogously we
  can consider inverse semigroup crossed products of arbitrary C*-algebras.
  For certain classes of Hausdorff groupoids there is a known dichotomy: th
 e groupoid C*-algebra is either stably finite or purely infinite. Allowing
  for inverse semigroup crossed products introduces non-trivial obstacles t
 o extending these results. We will outline the crossed product constructio
 n and present work towards the purely infinite-stably finite dichotomy. Jo
 int work with Becky Armstrong\, Lisa Clark\, Astrid an Huef and Diego Mart
 ı́nez.
LOCATION:External
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