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

@article{Ioana2012CartanSO,
title={Cartan subalgebras of amalgamated free product II\$\_1\$ factors},
journal={arXiv: Operator Algebras},
year={2012}
}
• A. Ioana
• Published 30 June 2012
• Mathematics
• arXiv: Operator Algebras
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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## References

SHOWING 1-10 OF 65 REFERENCES

• Mathematics
• 2014