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Von Neumann Algebras and Extensions of Inverse Semigroups
Published online by Cambridge University Press: 19 September 2016
Abstract
In the 1970s, Feldman and Moore classified separably acting von Neumann algebras containing Cartan maximal abelian self-adjoint subalgebras (MASAs) using measured equivalence relations and 2-cocycles on such equivalence relations. In this paper we give a new classification in terms of extensions of inverse semigroups. Our approach is more algebraic in character and less point-based than that of Feldman and Moore. As an application, we give a restatement of the spectral theorem for bimodules in terms of subsets of inverse semigroups. We also show how our viewpoint leads naturally to a description of maximal subdiagonal algebras.
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- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 1 , February 2017 , pp. 57 - 97
- Copyright
- Copyright © Edinburgh Mathematical Society 2016
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