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arXiv · 0904.1225

Strongly solid ${\rm II_1}$ factors with an exotic MASA

Cyril Houdayer·Dimitri Shlyakhtenko
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Abstract

Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid $\rm{II}_1$ factor $M$ containing an "exotic" maximal abelian subalgebra $A$: as an $A$,$A$-bimodule, $L^2(M)$ is neither coarse nor discrete. Thus we show that there exist $\rm{II}_1$ factors with such property but without Cartan subalgebras. It also follows from Voiculescu's free entropy results that $M$ is not an interpolated free group factor, yet it is strongly solid and has both the Haagerup property and the complete metric approximation property.

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Cyril Houdayer, Dimitri Shlyakhtenko. 2009-04-07. Strongly solid ${\rm II_1}$ factors with an exotic MASA. https://doi.org/10.1093/imrn%2Frnq117

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