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SUMMARY:Ali Raad
DTSTART:20210301T150000Z
DTEND:20210301T160000Z
DTSTAMP:20260423T021244Z
UID:GOBA/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOBA/22/">Ex
 istence and Uniqueness of Canonical Cartan Subalgebras in Inductive Limit 
 C*-algebras</a>\nby Ali Raad as part of Groups\, Operators\, and Banach Al
 gebras Webinar\n\n\nAbstract\nCartan subalgebras of C*-algebras have witne
 ssed major breakthroughs recently\, becoming the cornerstone of how to bui
 ld a bridge between C*-algebras on the one hand\, and geometric group theo
 ry and topological dynamics on the other. As such\, existence and uniquene
 ss questions become crucial. \n\nIn this talk I will introduce the notion 
 of a Cartan subalgebra and discuss the question of existence and uniquenes
 s in the setting of inductive limit C*-algebras. Indeed Stratila and Voicu
 lescu show in 1975 that AF-algebras admit a canonical Cartan subalgebra. I
  will provide a novel uniqueness result for the uniqueness of these subalg
 ebras in AF-algebras\, and also completely settle the question of existenc
 e and uniqueness of canonical Cartan subalgebras in AI-algebras and AT-alg
 ebras. If time permits\, I will generalize a theorem of Renault's that giv
 es a correspondence between Cartan pairs and C*-algebras of twisted étale
  groupoids.\n
LOCATION:https://researchseminars.org/talk/GOBA/22/
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