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Strongly solid II$$_{1}$$ factors with an exotic MASA. (English) Zbl 1220.46039
Summary: Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid 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 II$$_1$$ factors with this 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.

##### MSC:
 46L36 Classification of factors
##### Citations:
Zbl 1201.46054; Zbl 1213.46053
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