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Biexact von Neumann algebras
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abstract
We introduce the notion of biexactness for general von Neumann algebras, naturally extending the notion from group theory. We show that biexactness implies solidity for von Neumann algebras, and that many of the examples of solid von Neumann algebras contained in the literature are, in fact, biexact. We also give examples of certain crossed products arising from Gaussian actions that are solid but not biexact, and we give examples of certain $q$-Gaussian von Neumann algebras that are strongly solid but not biexact. The techniques developed involve studying a certain weak form of nuclear embeddings, and we use this setting to give a new description of weak exactness for von Neumann algebras, which allows us to answer several open problems in the literature about weakly exact von Neumann algebras.
Forward citations
Cited by 2 Pith papers
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W*-correlations of II$_1$ factors and rigidity of tensor products and graph products
Different subsets F of {2,3,...} give groups G_F whose von Neumann algebras are not W*-correlated, hence not measure equivalent nor W*-equivalent.
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On Relative Biexactness of Amalgamated Free Product von Neumann Algebras
Amalgamated free products of weakly exact tracial von Neumann algebras over injective amalgams are relatively biexact, and injective free products over a mixing amalgam are biexact.
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