Homology of Group Von Neumann Algebras

Simple item page
dc.contributor.authorMattox, Wadeen
dc.contributor.committeechairLinnell, Peter A.en
dc.contributor.committeememberThomson, James E.en
dc.contributor.committeememberFloyd, William J.en
dc.contributor.committeememberHaskell, Peter E.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:14:18Zen
dc.date.adate2012-08-08en
dc.date.available2014-03-14T20:14:18Zen
dc.date.issued2012-07-17en
dc.date.rdate2012-08-08en
dc.date.sdate2012-07-25en
dc.description.abstractIn 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.en
dc.description.degreePh. D.en
dc.identifier.otheretd-07252012-112602en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-07252012-112602/en
dc.identifier.urihttp://hdl.handle.net/10919/28397en
dc.publisherVirginia Techen
dc.relation.haspartMattox_WD_D_2012.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectgroup theoryen
dc.subjectgroup von neumann algebraen
dc.subjecthomologyen
dc.titleHomology of Group Von Neumann Algebrasen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Mattox_WD_D_2012.pdf
Size:
462.83 KB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations