## Structure of Factors and Automorphism Groups, Issue 51This book describes the recent development in the structure theory of von Neumann algebras and their automorphism groups. It can be viewed as a guided tour to the state of the art. |

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### Contents

1 | |

General Theory of Crossed Products and Duality | 33 |

Structure of Factors of Type III | 59 |

Connes Theory of Injective Factors and Automorphisms | 77 |

References | 101 |

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### Common terms and phrases

abelian group action of G algebra of type Arveson Aut(R automorphism group Borel C*-algebra called canonical central sequences centrally ergodic cocycle commute conditional expectation conditions are equivalent conjugacy conjugate construction COROLLARY covariant system crossed product decomposition deﬁned deﬁnition denote discrete dual duality theorem essential spectrum exists factors of type faithful semiﬁnite normal finite ﬁnite dimensional ﬁx ﬂow of weights following THEOREM group G Hence Hilbert space homomorphism inﬁnite injective factors Int(M isomorphic left Hilbert algebra LEMMA linear locally compact group modular automorphism group Neumann algebra nonsingular nonzero normal trace o-strongly o-weakly dense operator algebras Out(M parameter automorphism group projection Radon-Nikodym theorem representation of G satisﬁes selfadjoint semifinite semiﬁnite normal weight separable factor spectral strongly stable structure subalgebra T6hoku Math Takesaki tensor product Tomita-Takesaki theory unique unitary representation von Neumann algebra