Popa algebras in free group factors

By N. Brown, K. Dykema. 2002

56 citations recorded by the source corpus.

For each 1<s<\infty, a Popa algebra A_s is constructed that embeds as a weakly dense C*-subalgebra of the interpolated free group factor L(F_s). Certain approximation properties for A_s are shown. It follows that L(F_s) has the weak expectation property of Lance with respect to A_s. In the course of the demonstration, it is proved that under certain conditions, full amalgamated free products of matrix algebras are residually finite dimensional.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d826ce78ac71e31e7ca0c565be9aa48bbf31aa77

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Citations in the corpus

Tensor Products of C*-Algebras and Operator Spaces (2020, background): “More examples (where M is a free group factor and A a specially chosen weak*-dense Popa C∗subalgebra) appear in later papers by Brown and Dykema [37, 38].”
Free entropy dimension in amalgamated free products (2006, methodology): “Popa algebras and free group factors In [5] it was shown that for any 1 < s < ∞ there is a finitely generated, weakly dense Popa algebra As ⊂ L(Fs) such that L(Fs) has a weak expectation relative to As.”
ABOUT THE QWEP CONJECTURE (2003, background): “Since each τi is liftable, there is an asymptotically multiplicative and asymptotically trace preserving ucp map ϕi from Ai into a full matrix algebra Di. We claim that ϕi can be chosen exactly trace preserving and multiplicative on B. Indeed, by amplifying the range Di if necessary, we may assume t”