On the cohomology of joins of operator algebras
dc.contributor.advisor | Pearcy, Carl M. | |
dc.contributor.advisor | Smith, Roger R. | |
dc.creator | Husain, Ali-Amir | |
dc.date.accessioned | 2004-09-30T01:55:50Z | |
dc.date.available | 2004-09-30T01:55:50Z | |
dc.date.created | 2006-05 | |
dc.date.issued | 2004-09-30 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/377 | |
dc.description.abstract | The 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 |
dc.format.extent | 356432 bytes | en |
dc.format.extent | 112724 bytes | en |
dc.format.medium | electronic | en |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Texas A&M University | |
dc.subject | operator algebras | en |
dc.subject | Hochschild cohomology | en |
dc.subject | type I finite von Neumann algebras | en |
dc.title | On the cohomology of joins of operator algebras | en |
dc.type | Book | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A&M University | en |
thesis.degree.name | Doctor of Philosophy | en |
thesis.degree.level | Doctoral | en |
dc.contributor.committeeMember | Rediniotis, Othon K. | |
dc.contributor.committeeMember | Stiller, Peter F. | |
dc.type.genre | Electronic Dissertation | en |
dc.type.material | text | en |
dc.format.digitalOrigin | born digital | en |
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