## Kyoto Journal of Mathematics

### Cohomology for spatial superproduct systems

#### Abstract

We introduce a cohomology theory for spatial superproduct systems and compute the $2$-cocycles for some basic examples called Clifford superproduct systems, thereby distinguishing them up to isomorphism. This consequently proves that a family of $E_{0}$-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.

#### Article information

Source
Kyoto J. Math., Volume 59, Number 1 (2019), 53-75.

Dates
Revised: 26 December 2016
Accepted: 28 December 2016
First available in Project Euclid: 23 August 2018

https://projecteuclid.org/euclid.kjm/1534989637

Digital Object Identifier
doi:10.1215/21562261-2018-0002

Mathematical Reviews number (MathSciNet)
MR3934623

Zentralblatt MATH identifier
07081622

#### Citation

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

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