A class of II_1 factors with many non conjugate Cartan subalgebras

Details A class of II_1 factors with many non conjugate Cartan subalgebras A class of II_1 factors with many non conjugate Cartan subalgebras

2011-07-07

arxiv.org/abs/1107.1356v2

Mathematics

Operator Algebras

v2: we provide examples of II_1 factors M such that conjugacy of Cartan subalgebras of M by an automorphism, is a complete ana

Scientific paper

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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