## Abstract

If N⊂R^{ω} is a separable II_{1}-factor, the space H{double-struck}om(N,R^{ω}) of unitary equivalence classes of unital *-homomorphisms N→R; is shown to have a surprisingly rich structure. If N is not hyperfinite, Hom(N,R) is an infinite-dimensional, complete, metrizable topological space with convex-like structure, and the outer automorphism group Out(N) acts on it by "affine" homeomorphisms. (If NR, then Hom(N,R^{ω}) is just a point.) Property (T) is reflected in the extreme points - they're discrete in this case. For certain free products N=ς*R, every countable group acts nontrivially on H{double-struck}om(N,R^{ω}), and we show the extreme points are not discrete for these examples. Finally, we prove that the dynamical systems associated to free group factors are isomorphic.

Original language | English (US) |
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Pages (from-to) | 1665-1699 |

Number of pages | 35 |

Journal | Advances in Mathematics |

Volume | 227 |

Issue number | 4 |

DOIs | |

State | Published - Jul 10 2011 |

## All Science Journal Classification (ASJC) codes

- General Mathematics

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