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

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

2011-12-05

arxiv.org/abs/1112.0831v1

Mathematics

Operator Algebras

Scientific paper

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

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