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Mixing actions of the Heisenberg group

Published online by Cambridge University Press:  21 January 2013

ALEXANDRE I. DANILENKO
ALEXANDRE I. DANILENKO*
Affiliation:
Institute for Low Temperature Physics & Engineering of National Academy of Sciences of Ukraine, 47 Lenin Avenue, Kharkov, 61164, Ukraine email alexandre.danilenko@gmail.com
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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
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 4 , August 2014 , pp. 1142 - 1167
Copyright
©2013 Cambridge University Press 

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