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

Dani, S. G. ; Shah, Nimish A. ; Willis, George A. (2006) Locally compact groups with dense orbits under Zd-actions by automorphisms Ergodic Theory & Dynamical Systems, 26 (5). pp. 1443-1465. ISSN 0143-3857

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Related URL: http://dx.doi.org/10.1017/S0143385706000307

Abstract

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.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
ID Code:8250
Deposited On:26 Oct 2010 12:00
Last Modified:16 May 2016 18:17

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