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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.
- Type
- Research Article
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- Copyright
- ©2013 Cambridge University Press
References
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