zbMATH — the first resource for mathematics

A characterization of a coaction reduced to that of a closed subgroup. (English) Zbl 1156.46043
Summary: 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.
46L55 Noncommutative dynamical systems
Full Text: DOI
[1] H. Aoi and T. Yamanouchi, A characterization of coactions whose fixed-point algebras contain special maximal abelian \(\ast\)-subalgebras, Ergod. Th. & Dynam. Sys., 26 (2006), 1673-1706. · Zbl 1135.46038
[2] H. Aoi and T. Yamanouchi, On the normalizing groupoids and the commensurability groupoids for inclusions of factors associated to ergodic equivalence relations-subrelations, J. Funct. Anal., 240 (2006), 297-333. · Zbl 1122.28012
[3] K. Dykema, Crossed product decompositions of a purely infinite von Neumann algebra with faithful, almost periodic weight, Indiana Univ. Math. J., 44 (1995), no. 2, 433-450. · Zbl 0841.46048
[4] G. B. Folland, A Course in Abstract Harmonic Analysis , RC Press, Inc., 1995. · Zbl 0857.43001
[5] P. Hahn, The regular representations of measure groupoids, Trans. Amer. Math. Soc., 242 (1978), 35-72. · Zbl 0356.46055
[6] M. Izumi, Canonical extension of endomorphisms of type III factors, Amer. J. Math., 125 (2003), no. 1, 1-56. · Zbl 1037.46054
[7] M. B. Landstad, Twisted dual-group algebras: Equivalent reformations of \(C_0(G)\), J. Funct. Anal., 132 (1995), 43-85. · Zbl 0839.22003
[8] Y. Nakagami, Dual action on a von Neumann algebra and Takesaki’s duality for a locally compact group, Publ. RIMS, Kyoto Univ., 12 (1977), 727-775. · Zbl 0363.46062
[9] Y. Nakagami and M. Takesaki, Duality for crossed products of von Neumann algebras , Lecture Notes in Math. 731 , Springer-Verlag, 1979. · Zbl 0423.46051
[10] M. Takesaki, Duality for crossed products and the structure of von Neumann algebras of type III, Acta Math., 131 (1973), 249-310. · Zbl 0268.46058
[11] T. Yamanouchi, One-cocycles on smooth flows of weights and extended modular coactions, Ergod. Th. & Dynam. Sys., 27 (2007), 285-318. · Zbl 1152.46057
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.