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Rigidity of the measurable structure for algebraic actions of higher rank abelian groups

Boris Kalinin·Ralf Spatzier
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Abstract

We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy measure with Haar measures along the leaves. We deduce various rigidity theorems for isomorphisms and joinings as corollaries.

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Boris Kalinin, Ralf Spatzier. 2002-07-16. Rigidity of the measurable structure for algebraic actions of higher rank abelian groups. https://arxiv.org/abs/math/0207137

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