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arXiv · 1810.05267

Cartan Triples

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

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Allan P. Donsig, Adam H. Fuller, David R. Pitts. 2018-10-11. Cartan Triples. https://doi.org/10.1093/imrn%2Frnz340

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