Locally compact groups with dense orbits under �d-actions by automorphisms

Dani, S. G. and Shah, Nimish A. and Willis, George A. (2006) Locally compact groups with dense orbits under �d-actions by automorphisms. Ergodic Theory and Dynamical Systems, 26 (5). pp. 1443-1465.

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We consider locally compact groups G admitting a topologically transitive �d-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 �d-action and such that the �d-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
Uncontrolled Keywords: automorphisms, decomposition, isomorphic, topological
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 28 Sep 2012 12:05

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