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University of New Hampshire
Burnside factors, amenability defects and transitive families of projections in factors of type II(1)
Abstract
dc:description.abstract<p>We introduce a notion of transitive family of projections in a type II1 factor and prove that there exists (i) a 5 element transitive family in the hyperfinite II1 and (ii) a 12 element free transitive family. We then prove that the group von Neumann algebras of the known infinite free Burnside groups are all type II1 factors. Our investigation of weak-amenability properties of Burnside groups leads us to consider the Connes theory of correspondences. From this investigation we are able to define a new Folner invariant for type II1 factors. We prove a monotonicity result and find a positive lower bound for the free group factor L( F2 ).</p>
Degree
thesis:*- Name thesis:degree_name
- Doctor of Philosophy
- Level thesis:degree_level
- Dissertation
- Year
- 2005
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Bannon, Jon P
- Contributors dc:contributor
-
- Liming Ge
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Repository record dc:identifier
- https://scholars.unh.edu/dissertation/258
- OAI identifier oai:identifier
- oai:scholars.unh.edu:dissertation-1257