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arXiv · 1107.1356

A class of II_1 factors with many non conjugate Cartan subalgebras

An Speelman·Stefaan Vaes
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Abstract

We construct a class of II_1 factors M that admit unclassifiably many Cartan subalgebras in the sense that the equivalence relation of being conjugate by an automorphism of M is complete analytic, in particular non Borel. We also construct a II_1 factor that admits uncountably many non isomorphic group measure space decompositions, all involving the same group G. So G is a group that admits uncountably many non stably orbit equivalent actions whose crossed product II_1 factors are all isomorphic.

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An Speelman, Stefaan Vaes. 2012-07-02. A class of II_1 factors with many non conjugate Cartan subalgebras. https://arxiv.org/abs/1107.1356

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