CARTAN TRIPLES

Authors

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

Date of this Version

10-11-2018

Citation

2018 Authors

Comments

arXiv:1810.05267v1 [math.OA] 11 Oct 2018

Abstract

We introduce the class of Cartan triples as a generalization of the notion of a Car- tan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi’s theorem to this setting. This context contains that of Fulman’s generalization of Cartan MASAs and we discuss his generalization in an appendix.