| 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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| Files |
| Filename |
Size |
Approximate Download Time
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56K Modem |
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Mattox_WD_D_2012.pdf |
473.94 Kb |
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