# Cartan subalgebras of amalgamated free product II$_1$ factors

@article{Ioana2012CartanSO, title={Cartan subalgebras of amalgamated free product II\$\_1\$ factors}, author={Adrian Ioana}, journal={arXiv: Operator Algebras}, year={2012} }

We study Cartan subalgebras in the context of amalgamated free product II$_1$ factors and obtain several uniqueness and non-existence results. We prove that if $\Gamma$ belongs to a large class of amalgamated free product groups (which contains the free product of any two infinite groups) then any II$_1$ factor $L^{\infty}(X)\rtimes\Gamma$ arising from a free ergodic probability measure preserving action of $\Gamma$ has a unique Cartan subalgebra, up to unitary conjugacy. We also prove that if…

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