Document Type

Dissertation

Date of Degree

Summer 2012

Degree Name

PhD (Doctor of Philosophy)

Degree In

Mathematics

First Advisor

Paul Muhly

Second Advisor

Ionut Chifan

Abstract

This work contains some structural results for von Neumann algebras arising from measure preserving actions by direct products of groups on probability spaces. The technology and the methods we use are a continuation of those used by Chifan and Sinclair in [10]. By employing these methods, we obtain new examples of strongly solid factors as well as von Neumann algebras with unique or no Cartan subalgebra. We show for instance that every II 1 factor associated with a weakly amenable group in the class S of Ozawa is strongly solid [59]. We also obtain a product version of this result: any maximal abelian ∗-subalgebra of any II 1 factor associated with a finite direct product of weakly amenable groups in the class S of Ozawa has an amenable normalizing algebra. Finally, pairing some of these results with Ioana's cocycle superrigidity theorem [36], we prove that compact actions by finite products of lattices in Sp(n, 1), n ≥ 2, are virtually W∗-superrigid. The results presented here are joint work with Ionut Chifan and Thomas Sinclair. They constitute the substance of an article [11] which has already been submitted for publication.

Keywords

C∗-algebras, ergodic theory, hyperbolic groups, von Neumann algebras

Pages

v, 74 pages

Bibliography

Includes bibliographical references (pages 68-74).

Copyright

Copyright 2012 Bogdan Teodor Udrea

Included in

Mathematics Commons

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