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Ilija Tolich (Victoria University of Wellington)
Friday 04 July 2025, 14:30-15:00
Stably finite and purely infinite crossed products
- ๐ค Speaker: Ilija Tolich (Victoria University of Wellington)
- ๐ Date & Time: Friday 04 July 2025, 14:30 - 15:00
- ๐ Venue: External
Abstract
The C-algebra associated to a topological groupoid can be viewed as a crossed product: by the partial action of the inverse semigroup of 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: the groupoid C*-algebra is either stably finite or purely infinite. Allowing for inverse semigroup crossed products introduces non-trivial obstacles to extending these results. We will outline the crossed product construction and present work towards the purely infinite-stably finite dichotomy. Joint work with Becky Armstrong, Lisa Clark, Astrid an Huef and Diego Martฤฑฬnez.
Series This talk is part of the Isaac Newton Institute Seminar Series series.
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