- Title
- Locally compact groups with dense orbits under ℤd-actions by automorphisms
- Creator
- Dani, S. G.; Shah, Nimish A.; Willis, George A.
- Relation
- Ergodic Theory and Dynamical Systems Vol. 26, Issue 5, p. 1443-1465
- Publisher Link
- http://dx.doi.org/10.1017/S0143385706000307
- Publisher
- Cambridge University Press
- Resource Type
- journal article
- Date
- 2006
- Description
- We consider locally compact groups G admitting a topologically transitive ℤd-action by automorphisms. It is shown that such a group G has a compact normal subgroup K of G, invariant under the action, such that G/K is a product of (finitely many) locally compact fields of characteristic zero; moreover, the totally disconnected fields in the decomposition can be chosen to be invariant under the ℤd-action and such that the ℤd-action is via scalar multiplication by non-zero elements of the field. Under the additional conditions that G be finite dimensional and ‘locally finitely generated’ we conclude that K as above is connected and contained in the center of G. We describe some examples to point out the significance of the conditions involved.
- Subject
- automorphisms; decomposition; isomorphic; topological
- Identifier
- uon:6397
- Identifier
- http://hdl.handle.net/1959.13/803448
- Identifier
- ISSN:0143-3857
- Full Text
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