{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/53956"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/53956","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Zero Divisors, Group Von Neumann Algebras and Injective Modules","abstract":"In 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. 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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. 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