A characterization of a coaction reduced to that of a closed subgroup.

*(English)*Zbl 1156.46043Summary: It is shown that, for any coaction a of a locally compact group \(K\) on a properly infinite von Neumann algebra \(A\) and a closed subgroup \(H\) of \(K\), \(\alpha\) is cocycle conjugate to a coaction which comes from a coaction of \(H\) if and only if the dual action \(\widehat\alpha\) is induced by an action of \(H\). We also include applications of the result concerning almost periodic coactions and the ranges of 1-cocycles on measured equivalence relations.

##### MSC:

46L55 | Noncommutative dynamical systems |

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##### References:

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