Hokkaido Mathematical Journal

An example of a solid von Neumann algebra

Narutaka OZAWA

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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 $\mathrm{SL}L(2,\mathbb Z)$ on the Higson corona of $\mathbb Z^2$.

Article information

Source
Hokkaido Math. J. Volume 38, Number 3 (2009), 557-561.

Dates
First available: 18 November 2009

Permanent link to this document
http://projecteuclid.org/euclid.hokmj/1258553976

Mathematical Reviews number (MathSciNet)
MR2548235

Zentralblatt MATH identifier
05606280

Digital Object Identifier
doi:10.14492/hokmj/1258553976

Subjects
Primary: 46L35: Classifications of $C^*$-algebras
Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 37A20: Orbit equivalence, cocycles, ergodic equivalence relations

Keywords
solid von Neumann algebra amenable action

Citation

OZAWA, Narutaka. An example of a solid von Neumann algebra. Hokkaido Mathematical Journal 38 (2009), no. 3, 557--561. doi:10.14492/hokmj/1258553976. http://projecteuclid.org/euclid.hokmj/1258553976.


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