Concrete Classification and Centralizers of Certain $\mathbb{Z}^2 \rtimes {\rm SL}(2,\mathbb{Z})$ -actions

preprint2012arXivOpen access

We introduce a new class of actions of the group $\G$ on finite von Neumann algebras and call them twisted Bernoulli shift actions. We classify these actions up to conjugacy and give an explicit description of their centralizers. We also distinguish many of those actions on the AFD $\mathrm{II}_1$ factor in view of outer conjugacy.

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Concrete Classification and Centralizers of Certain $\mathbb{Z}^2 \rtimes {\rm SL}(2,\mathbb{Z})$ -actions

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Concrete Classification and Centralizers of Certain Z2⋊SL(2,Z)\mathbb{Z}^2 \rtimes {\rm SL}(2,\mathbb{Z})Z2⋊SL(2,Z)-actions

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Concrete Classification and Centralizers of Certain $\mathbb{Z}^2 \rtimes {\rm SL}(2,\mathbb{Z})$ -actions