Isomorphism and Measure Rigidity for Algebraic Actions on Zero-Dimensional Groups |
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Authors: | Manfred Einsiedler |
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Institution: | (1) University of Washington, Seattle, WA, USA |
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Abstract: | We consider mixing d-actions on compact zero-dimensional abelian groups by automorphisms. Rigidity of invariant measures does not hold for such actions in general; we present conditions which force an invariant measure to be Haar measure on an affine subset. This is applied to isomorphism rigidity for such actions. We develop a theory of halfspace entropies which plays a similar role in the proof to that played by invariant foliations in the proof of rigidity for smooth actions. |
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Keywords: | 2000 Mathematics Subject Classification: 37A35 37A45 37B50 13E05 |
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