Title page for ETD etd-07252012-112602


Type of Document Dissertation
Author Mattox, Wade
URN etd-07252012-112602
Title Homology of Group Von Neumann Algebras
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Linnell, Peter A. Committee Chair
Floyd, William J. Committee Member
Haskell, Peter E. Committee Member
Thomson, James E. Committee Member
Keywords
  • group theory
  • group von neumann algebra
  • homology
Date of Defense 2012-07-17
Availability unrestricted
Abstract
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.
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