Cohomology for spatial superproduct systems

摘要

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 ofE0-semigroups on type III factors, whichwe callCARflows, are noncocycle-conjugate for different ranks. Similar results followfor the evenCARflows aswell.We also compute the automorphism group of the Clifford superproduct systems.