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Mixing actions of the Heisenberg group
Published online by Cambridge University Press: 21 January 2013
Abstract
Mixing (of all orders) rank-one actions $T$ of the Heisenberg group ${H}_{3} ( \mathbb{R} )$ are constructed. The restriction of $T$ to the center of ${H}_{3} ( \mathbb{R} )$ is simple and commutes only with $T$. Mixing Poisson and mixing Gaussian actions of ${H}_{3} ( \mathbb{R} )$ are also constructed. A rigid weakly mixing rank-one action $T$ is constructed such that the restriction of $T$ to the center of ${H}_{3} ( \mathbb{R} )$ is not isomorphic to its inverse.
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