Abstract
To a real Hilbert space and a one-parameter group of orthogonal transformations we associate a C∗-algebra which admits a free quasi-free state. This construction is a freeprobability analog of the construction of quasi-free states on the CAR and CCR algebras. We show that under certain conditions, our C∗-algebras are simple, and the free quasi-free states are unique. The corresponding von Neumann algebras obtained via the GNS construction are free analogs of the Araki-Woods factors. Such von Neumann algebras can be decomposed into free products of other von Neumann algebras. For non-trivial one-parameter groups, these von Neumann algebras are type III factors. In the case the one-parameter group is nontrivial and almost-periodic, we show that Connes’ Sd invariant completely classifies these algebras.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
