Concrete classification and centralizers of certain \(\mathbb Z^2 \rtimes SL (2,\mathbb Z)\)-actions. (English) Zbl 1201.46061

Summary: We introduce a new class of actions of the group \({\mathbb Z}^{2} \rtimes {SL}(2,{\mathbb Z})\) 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 II\(_{1}\) factor in view of outer conjugacy.


46L55 Noncommutative dynamical systems
46L40 Automorphisms of selfadjoint operator algebras
46L10 General theory of von Neumann algebras
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