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DTSTART:20211107T020000
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UID:calendar.24842.field_event_date_2.0@math.wustl.edu
CREATED:20210830T180544Z
DESCRIPTION:Abstract: Groupoid operator algebras are of important objects,
since on the one hand they link the field of C*-algebra and von Neumann a
lgebra to other areas like geometry and dynamics and on the other hand des
cribe important structural features of operator algebras themselves. To ev
ery étale groupoid with locally compact Hausdorff space of units, one can
associate an essential groupoid C*-algebra, which is a suitable quotient
of the reduced groupoid C*-algebra by an ideal of singular elements. For
Hausdorff groupoids, it equals the reduced groupoid C*-algebra. Until re
cently, it had been an open question to characterise simplicity of such e
ssential groupoid C*-algebras. Even in for Hausdorff groupoids, only part
ial results were known.\n \n In this talk, I will report on joint work with
Matthew Kenney, Se-Jin Kim, Xin Li and Dan Ursu, which characterises é
tale groupoids with locally compact Hausdorff space of units whose essenti
al groupoid C*-algebra is has the ideal intersection property. Our charact
erisation is phrased in terms of what is called essentially confined amena
ble sections of isotropy groups, a notion that can be checked in concrete
cases. This provides a complete solution of the open problem, combining
the ideal intersection property with the dynamical requirement of minimali
ty. In particular, it comes as a surprise that non-Hausdorff groupoids fi
t well into this general picture. Our work extends and unifies previous re
sults among others on C*-simplicty of discrete groups, their topological
dynamical systems and groupoids of germs. \n\nHost: Xiang Tang
DTSTART;TZID=America/Chicago:20211018T150000
DTEND;TZID=America/Chicago:20211018T160000
LAST-MODIFIED:20211004T141913Z
SUMMARY:Analysis Seminar: 'Simplicity and the ideal intersection property f
or essential groupoid C*-algebras'
URL;TYPE=URI:https://math.wustl.edu/events/analysis-seminar-simplicity-and-
ideal-intersection-property-essential-groupoid-c-algebras
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