KolloquiumGRK Generalizing inductive limits in C*-algebras |  |
Speaker:JProf. Dr. Kristin Courtney, WWU Münster
Location:Mathematisches Institut, Bunsenstr 3-5SitzungszimmerZoom: https://uni-goettingen.zoom.us/j/91336854872 Live Stream: http://streaming.math.uni-goettingen.de/Gras Geo Map
Organizer:Fakultät für Mathematik und Informatik
Details:
Inductive limits are a central construction in C*-theory because they allow one to use well-understood building blocks to naturally construct intricate C*-algebras whose properties remain tractable. One task for the structural theory of operator algebras is to determine which classes of operator algebras arise as inductive limits of nice operator algebras.
The model result in this direction is Connes' 1970's theorem showing that many classes of von Neumann algebras, including semi-discrete von Neumann algebras, arise as inductive limits of finite dimensional von Neumann algebras. For C*-algebras, an analogous result fails outright: many nuclear C*-algebras are not inductive limits of finite dimensional C*-algebras. However, by generalizing our notion of an inductive system, we can in fact describe any nuclear C*-algebra as the limit of system of finite dimensional C*-algebras. This is based on joint work with Wilhelm Winter.
The model result in this direction is Connes' 1970's theorem showing that many classes of von Neumann algebras, including semi-discrete von Neumann algebras, arise as inductive limits of finite dimensional von Neumann algebras. For C*-algebras, an analogous result fails outright: many nuclear C*-algebras are not inductive limits of finite dimensional C*-algebras. However, by generalizing our notion of an inductive system, we can in fact describe any nuclear C*-algebra as the limit of system of finite dimensional C*-algebras. This is based on joint work with Wilhelm Winter.
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Type:Colloquium
Language:English
Category:Research
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Direct link to event:https://events.goettingen-campus.de/event?eventId=29096
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