Mathematics – Operator Algebras
Scientific paper
2009-04-07
Int. Math. Res. Not. IMRN 2011, no. 6, 1352-1380
Mathematics
Operator Algebras
23 pages
Scientific paper
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.
Houdayer Cyril
Shlyakhtenko Dimitri
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