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We classify, up to stable conjugacy, centrally ergodic actions α of R on an injective semifinite von Neumann algebra with an invariant trace and with Γ(α) = R. We also classify actions of R on an injective semifinite von Neumann algebra with a non-trivial center, and which admit an invariant trace.

Centrally ergodic one-parameter automorphism groups on semifinite injective von Neumann algebras.