Homology of Group Von Neumann Algebras

In this paper the following conjecture is studied: the group von Neumann algebra N(G) is a flat CG-module if and only if the group G is locally virtually cyclic. This paper proves that if G is locally virtually cyclic, then N(G) is flat as a CG-module. The converse is proved for the class of all elementary amenable groups without infinite locally finite subgroups. Foundational cases for which the conjecture is shown to be true are the groups G=Z, G=ZxZ, G=Z*Z, Baumslag-Solitar groups, and some infinitely-presented variations of Baumslag-Solitar groups. Modules other than N(G), such as L^p-spaces and group C*-algebras, are considered as well. The primary tool that is used to achieve many of these results is group homology.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2012

Author dc:creator

• Mattox, Wade

Chair dc:contributor.committeechair

• Linnell, Peter A.

Committee members dc:contributor.committeemember

• Thomson, James E.
• Floyd, William J.
• Haskell, Peter E.

• group theory
• group von neumann algebra
• homology

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-07252012-112602

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28397