Locally compact groups with dense orbits under ℤd-actions by automorphisms

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
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