On the cohomology of joins of operator algebras /
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| Other Authors: | , |
| Format: | Thesis eBook |
| Language: | English |
| Published: |
[College Station, Tex.] :
[Texas A&M University],
[2004]
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| Subjects: | |
| Online Access: | Link to OAK Trust copy |
| 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. |
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| Item Description: | "Major Subject: Mathematics" Title from author supplied metadata (record created on Nov. 30, 2005.) Vita. Abstract. Electronic resource. |
| Physical Description: | 1 online resource. |
| Format: | System requirements: Adobe Acrobat Reader. |
| Bibliography: | Includes bibliographical references. |