Mixing actions of Heisenberg group

Details Mixing actions of Heisenberg group Mixing actions of Heisenberg group

2011-12-22

arxiv.org/abs/1112.5248v1

Mathematics

Dynamical Systems

Scientific paper

Mixing (of all orders) rank-one actions $T$ of Heisenberg group $H_3(\Bbb R)$ are constructed. The restriction of $T$ to the center of $H_3(\Bbb R)$ is simple and commutes only with $T$. Mixing Poisson and mixing Gaussian actions of $H_3(\Bbb R)$ are also constructed. A rigid weakly mixing rank-one action $T$ is constructed such that the restriction of $T$ to the center of $H_3(\Bbb R)$ is not isomorphic to its inverse.

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