An introduction to von Neumann algebras II

Adrian Ioana
University of California, San Diego (UCSD)

The goal of this tutorial is to give an introduction to von Neumann algebras. After recalling the basic definitions, I will present the construction of von Neumann algebras arising from countable groups and their measure preserving actions. I will then explain how analytic properties of groups (amenability, property (T)) are used to obtain classification and rigidity results for von Neumann algebras. Finally, I will discuss the ultraproduct construction for von Neumann algebras and related open problems.

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