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

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

2007-04-12

arxiv.org/abs/0704.1533v3

J. Math. Soc. Japan 62 (2010), no. 1, 135-166

Mathematics

Operator Algebras

24pages, the title was changed, Chap 6 was added

Scientific paper

10.2969/jmsj/06210135

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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