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arXiv · 1112.0831

Compact actions and uniqueness of the group measure space decomposition of II$_1$ factors

Adrian Ioana
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Abstract

We prove that any II$_1$ factor $L^{\infty}(X)\rtimesΓ$ arising from a compact, free, ergodic, probability measure preserving action of a countable group $Γ$ with positive first $\ell^2$-Betti number, has a unique group measure space Cartan subalgebra, up to unitary conjugacy.

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Adrian Ioana. 2011-12-05. Compact actions and uniqueness of the group measure space decomposition of II$_1$ factors. https://arxiv.org/abs/1112.0831

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