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SUMMARY:Kristin Courtney (Univ. Muenster)
DTSTART:20210610T173000Z
DTEND:20210610T181500Z
DTSTAMP:20260423T004515Z
UID:Opalg21/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Opalg21/16/"
 >Nuclearity and generalized inductive limits</a>\nby Kristin Courtney (Uni
 v. Muenster) as part of Conference on operator algebras and related topics
  in Istanbul\, 2021\n\n\nAbstract\nOne of Alain Connes' seminal results es
 tablishes that any semi-discrete (or injective or amenable) von Neumann al
 gebra can be written as a direct limit of dimensional von Neumann algebras
 . In the C*-setting however\, such a concise characterization is not possi
 ble: the direct C*-analogue of semi-discreteness is nuclearity\, and most 
 nuclear C*-algebras do not arise as the direct limits of finite dimensiona
 l C*-algebras. Nonetheless\, by generalizing the notion of inductive limit
 s of C*-algebras\, Blackadar and Kirchberg were able to characterize quasi
 diagonal nuclear C*-algebras as those arising as (generalized) inductive l
 imits of finite dimensional C*-algebras. In joint work with Wilhelm Winter
 \, we give a further generalization of this construction\, which gives us 
 a complete characterization of separable nuclear C*-algebras as those aris
 ing from a (generalized) inductive limit of finite dimensional C*-algebras
 .\n
LOCATION:https://researchseminars.org/talk/Opalg21/16/
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