On automorphism groups acting ergodically on connected locally compact groups (Q2736863)
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scientific article; zbMATH DE number 1644966
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On automorphism groups acting ergodically on connected locally compact groups |
scientific article; zbMATH DE number 1644966 |
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11 September 2001
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ergodic automorphism group
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locally compact group
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On automorphism groups acting ergodically on connected locally compact groups (English)
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The author shows that a connected Lie group admitting an ergodic group of Lie automorphisms is nilpotent. Main theorem: Let \(G\) be a connected finite-dimensional locally compact group. Suppose that the action of the group \(\Aut (G)\) of all bicontinuous automorphisms of \(G\) on \(G\) has a dense orbit. Then \(G\) is nilpotent. Some extensions of this result and examples are discussed.
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