VON NEUMANN ALGEBRAS AND EXTENSIONS OF INVERSE SEMIGROUPS

Authors

Allan P. Donsig, University of Nebraska-LincolnFollow
Adam H. Fuller, University of Nebraska - LincolnFollow
David R. Pitts, University of Nebraska - LincolnFollow

Date of this Version

2017

Citation

Proceedings of the Edinburgh Mathematical Society (2017) 60, 57-97

Comments

Copyright 2016 The Edinburgh Mathematical Society

DOI: 10.1017/S0013091516000183

Abstract

In the 1970s, Feldman and Moore classified separably acting von Neumann algebras containing Cartan MASAs using measured equivalence re- lations 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.