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arXiv · 1409.1624

Von Neumann Algebras and Extensions of Inverse Semigroups

Allan P. Donsig·Adam H. Fuller·David R. Pitts
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Abstract

In the 1970s, Feldman and Moore classified separably acting von Neumann algebras containing Cartan 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-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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Allan P. Donsig, Adam H. Fuller, David R. Pitts. 2014-09-04. Von Neumann Algebras and Extensions of Inverse Semigroups. https://arxiv.org/abs/1409.1624

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