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Zero Divisors, Group Von Neumann Algebras and Injective Modules

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dc.contributor.authorRoman, Ahmed Hemdanen
dc.contributor.committeechairLinnell, Peter A.en
dc.contributor.committeememberMihalcea, Constantin Leonardoen
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2015-06-30T08:02:57Zen
dc.date.available2015-06-30T08:02:57Zen
dc.date.issued2015-06-29en
dc.description.abstractIn this thesis we discuss linear dependence of translations which is intimately related to the zero divisor conjecture. We also discuss the square integrable representations of the generalized Wyle-Heisenberg group in 𝑛² dimensions and its relations with Gabor's question from Gabor Analysis in the light of the time-frequency equation. We study the zero divisor conjecture in relation to the reduced 𝐶*-algebras and operator norm 𝐶*-algebras. For certain classes of groups we address the zero divisor conjecture by providing an isomorphism between the the reduced 𝐶*-algebra and the operator norm 𝐶*-algebra. We also provide an isomorphism between the algebra of weak closure and the von Neumann algebra under mild conditions. Finally, we prove some theorems about the injectivity of some spaces as ℂ𝐺 modules for some groups 𝐺.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:5415en
dc.identifier.urihttp://hdl.handle.net/10919/53956en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectaffine groupen
dc.subjectleft translationsen
dc.subjectlinear independenceen
dc.subjectsquare integrable representationen
dc.subjectzero divisor conjectureen
dc.subjectinjective moduleen
dc.subjectFourier transformen
dc.subjectC*-algebraen
dc.titleZero Divisors, Group Von Neumann Algebras and Injective Modulesen
dc.title.alternativeZero Divisors and Linear Independence of Translatesen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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