Hokkaido Mathematical Journal

OZAWA Narutaka,

An example of a solid von Neumann algebra.

Hokkaido Mathematical Journal, 38 (2009) pp.557-561

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Abstract

We prove that the group-measure-space von Neumann algebra $L^\infty(\mathbb T^2) \rtimes \mathrm{SL}(2,\mathbb Z)$ is solid. The proof uses topological amenability of the action of $\mathrm{SL}(2,\mathbb Z)$ on the Higson corona of $\mathbb Z^2$.

MSC(Primary)46L35
MSC(Secondary)43A07, 37A20
Uncontrolled Keywordssolid von Neumann algebra, amenable action.