Automorphisms that commute with a modular automorphism
type: Item
instance of: scholarly article
title: Automorphisms that commute with a modular automorphism
zbMATH Open document ID: 0581.46052
DOI: 10.1007/BF00400980
author: Heide Narnhofer
published in: Letters in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: It might be expected that the existence of automorphisms of the \(C^*\)- algebra A of quantum statistics that commute with the time automorphism, can give some insight into ergodic properties, as the existence of independent constants of motion do in classical dynamics. It turns out that the question whether such automorphisms exist cannot be decided on the level of the von Neumann algebra corresponding to the representation of A in some equilibrium state: in contrary: as all modular automorphisms of a von Neumann algebra are connected by inner cocycles, it is also possible to find to any automorphism group \(\sigma\) that commutes with some modular automorphism group \(\alpha_ t\) an inner cocycle such that the resulting automorphism group \({\bar \sigma}\) commutes with another given modular automorphism group \({\bar \alpha}{}_ t\).
Mathematics Subject Classification ID: 46L40
Mathematics Subject Classification ID: 46L55
Mathematics Subject Classification ID: 46L35
zbMATH DE Number: 3929728
zbMATH Keywords: existence of automorphisms of the \(C^*\)-algebra A of quantum statistics that commute with the time automorphism
zbMATH Keywords: ergodic properties
zbMATH Keywords: existence of independent constants of motion
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: modular automorphism group
MaRDI profile type: Publication
cites work: Q3969402
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cites work: Duality for crossed products and the structure of von Neumann algebras of type III
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description: scientific article; zbMATH DE number 3929728