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Centrally ergodic one-parameter automorphism groups on semifinite injective von Neumann algebras. (English) Zbl 0674.46037
Math. Scand. (to appear).
We classify, up to stable conjugacy, centrally ergodic actions \(\alpha\) of \({\mathbb{R}}\) with the Connes spectrum \(\Gamma(\alpha)\neq {\mathbb{R}}\) on injective semifinite factors. The complete invariants for stable conjugacy are the type of the crossed product algebra and the flow given by the dual action on the center of the crossed product algebra. Connes’ discrete decomposition technique and Krieger’s cohomology lemma are the key tools. We also exhibit actions for several pairs of invariants. As an application, we classify actions of \({\mathbb{R}}\) on an injective semifinite von Neumann algebra with a non-trivial center, and which admit an invariant trace, by Takesaki duality.
Reviewer: Y.Kawahigashi

MSC:
46L55 Noncommutative dynamical systems
46L10 General theory of von Neumann algebras
46L80 \(K\)-theory and operator algebras (including cyclic theory)
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