Prime Type III Factors

Mathematics – Operator Algebras

Scientific paper

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Scientific paper

10.1073/pnas.220417397

We show that for each (0<\lambda <1), the free Araki-Woods factor of type
III(_{\lambda}) cannot be written as a tensor product of two diffuse von
Neumann algebras (i.e., is prime), and does not contain a Cartan subalgebra.

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