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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.

46L36 Classification of factors
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