Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 59, Number 1 (2019), 53-75.
Cohomology for spatial superproduct systems
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.
Kyoto J. Math., Volume 59, Number 1 (2019), 53-75.
Received: 2 August 2016
Revised: 26 December 2016
Accepted: 28 December 2016
First available in Project Euclid: 23 August 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
Secondary: 46L40: Automorphisms 46L53: Noncommutative probability and statistics 46C99: None of the above, but in this section
Margetts, Oliver T.; Srinivasan, R. Cohomology for spatial superproduct systems. Kyoto J. Math. 59 (2019), no. 1, 53--75. doi:10.1215/21562261-2018-0002. https://projecteuclid.org/euclid.kjm/1534989637