Von Neumann Algebras and Extensions of Inverse Semigroups
Operator Algebras
2014-11-27 v2
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.
Keywords
Cite
@article{arxiv.1409.1624,
title = {Von Neumann Algebras and Extensions of Inverse Semigroups},
author = {Allan P. Donsig and Adam H. Fuller and David R. Pitts},
journal= {arXiv preprint arXiv:1409.1624},
year = {2014}
}
Comments
Applications added: i) a reformulation of the spectral theorem for Bures-closed bimodules and ii) a description of maximal subdiagonal algebras. 38 pages