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arXiv · 1305.3225

Normalizers inside amalgamated free product von Neumann algebras

Stefaan Vaes
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Abstract

Recently, Adrian Ioana proved that all crossed products by free ergodic probability measure preserving actions of a nontrivial free product group \Gamma_1 * \Gamma_2 have a unique Cartan subalgebra up to unitary conjugacy. Ioana deduced this result from a more general dichotomy theorem on the normalizer N_M(A)'' of an amenable subalgebra A of an amalgamated free product von Neumann algebra M = M_1 *_B M_2. We improve this dichotomy theorem by removing the spectral gap assumptions and obtain in particular a simpler proof for the uniqueness of the Cartan subalgebra in crossed products by \Gamma_1 * \Gamma_2.

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Stefaan Vaes. 2013-05-14. Normalizers inside amalgamated free product von Neumann algebras. https://arxiv.org/abs/1305.3225

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