We introduce a cohomology theory for spatial superproduct systems and compute the -cocycles for some basic examples called Clifford superproduct systems, thereby distinguishing them up to isomorphism. This consequently proves that a family of -semigroups on type III factors, which we call CAR flows, are noncocycle-conjugate for different ranks. Similar results follow for the even CAR flows as well. We also compute the automorphism group of the Clifford superproduct systems.
"Cohomology for spatial superproduct systems." Kyoto J. Math. 59 (1) 53 - 75, April 2019. https://doi.org/10.1215/21562261-2018-0002