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- W2048885061 abstract "Synopsis We consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already ergodic when restricted to A , and then, as a generalisation, the case of (not necessarily ergodic) actions of E with the property that the restriction to A is an action with abelian atomic fixed-point algebra. Both these cases are handled for general locally compact-countable G . Finally, we combine the obtained results to classify the ergodic actions of E when G is finite, provided that either the extension is central and Hom ( G , T) = 0, or G is abelian and either cyclic or of an order not divisible by a square." @default.
- W2048885061 created "2016-06-24" @default.
- W2048885061 creator A5041078483 @default.
- W2048885061 date "1989-01-01" @default.
- W2048885061 modified "2023-09-27" @default.
- W2048885061 title "Ergodic actions of group extensions on von Neumann algebras" @default.
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- W2048885061 doi "https://doi.org/10.1017/s0308210500028183" @default.
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