Kyoto Journal of Mathematics

Cohomology for spatial superproduct systems

Oliver T. Margetts and R. Srinivasan

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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 E0-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

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

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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

∗-endomorphisms $E_{0}$-semigroups type III factors noncommutative probability superproduct systems


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.

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