Cartan Triples
arXiv:1810.05267 · doi:10.1093/imrn/rnz340
Abstract
We introduce the class of Cartan triples as a generalization of the notion of a Cartan 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.
arXiv comment37 pages
References in corpus (5)
- Noncommutative Cartan sub-algebras of C*-algebras
- Bimodules over Cartan MASAs in von Neumann Algebras, Norming Algebras, and Mercer's Theorem
- C*-crossed products by partial actions and actions of inverse semigroups
- Structure for Regular Inclusions
- Isomorphisms of Lattices of Bures-Closed Bimodules over Cartan MASAs