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dc.contributor.advisorPearcy, Carl M.en_US
dc.contributor.advisorSmith, Roger R.en_US
dc.creatorHusain, Ali-Amiren_US
dc.date.accessioned2004-09-30T01:55:50Z
dc.date.available2004-09-30T01:55:50Z
dc.date.created2006-05en_US
dc.date.issued2004-09-30
dc.identifier.urihttp://hdl.handle.net/1969.1/377
dc.description.abstractThe algebra of matrices M with entries in an abelian von Neumann algebra is a C*-module. C*-modules were originally defined and studied by Kaplansky and we outline the foundations of the theory and particular properties of M. Furthermore, we prove a structure theorem for ultraweakly closed submodules of M, using techniques from the theory of type I finite von Neumann algebras. By analogy with the classical join in topology, the join for operator algebras A and B acting on Hilbert spaces H and K, respectively, was defined by Gilfeather and Smith. Assuming that K is finite dimensional, Gilfeather and Smith calculated the Hochschild cohomology groups of the join. We assume that M is the algebra of matrices with entries in a maximal abelian von Neumann algebra U, A is an operator algebra acting on a Hilbert space K, and B is an ultraweakly closed subalgebra of M containing U. In this new context, we redefine the join, generalize the calculations of Gilfeather and Smith, and calculate the cohomology groups of the join.en_US
dc.format.extent356432 bytes
dc.format.extent112724 bytes
dc.format.mediumelectronicen_US
dc.format.mimetypeapplication/pdf
dc.format.mimetypetext/plain
dc.language.isoen_USen_US
dc.publisherTexas A&M Universityen_US
dc.subjectoperator algebrasen_US
dc.subjectHochschild cohomologyen_US
dc.subjecttype I finite von Neumann algebrasen_US
dc.titleOn the cohomology of joins of operator algebrasen_US
dc.typeBooken
dc.typeThesisen
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorTexas A&M Universityen_US
thesis.degree.nameDoctor of Philosophyen_US
thesis.degree.levelDoctoralen_US
dc.contributor.committeeMemberRediniotis, Othon K.en_US
dc.contributor.committeeMemberStiller, Peter F.en_US
dc.type.genreElectronic Dissertationen_US
dc.type.materialtexten_US
dc.format.digitalOriginborn digitalen_US


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