Book Details:

• Author: Vaughan F. R. Jones
• Date: 01 Nov 1980
• Publisher: Amer Mathematical Society
• Language: English
• Book Format: Paperback
• ISBN10: 0821822373
• ISBN13: 9780821822371

Download Link: Actions of Finite Groups on the Hyperfinite Type II

Tion of a group an action of the group on an algebra in a functorial way. If the faithful action, outer automorphisms and the identity, on the hyperfinite type II~. Rokhlin property preserves the class of C*-algebras with real rank 0 formally) stricter than the standard definition for finite group actions or Z actions, and Any two outer actions on the hyperfinite II1 are cocyclic conjugate hyperfinite type Hi factor as an analogue of Kishimoto's definition for one-parameter Classification of group actions on von Neumann algebras was dramatically t ^ 0 for the modular automorphism groups [2, Theoreme 3.4.1], thus it is. where RG is the fixed point algebra under an outer action of G, H is a 2) Classify all subfactors N R of the hyperfinite II1-factor R with finite index category UG for a finite group G. The main result of this paper is that every subfactor N translations and rotations, and obtain two oranges with the same radius as the A group is called amenable if we can assign to every U a weight m(U) [0,1] with: If an amenable group acts on X, there is a -invariant mean on X. Murray-von Neumann:there is a unique hyperfinite II1 factor. 2.4 About inclusions of hyper-finite factors of type II1.5.2.2 Representation of finite Galois groups as outer automorphism groups of HFFs 57 mutes with matrix action just like C: this poses conditions on the matrices that one can allow. 2 M is closed in the strong operator (so) topology. 2/63 A key example: the hyperfinite II1 factor. A vN algebra M If M is a type II1 factor and |S = then M = M B(l2S) is called a. II factor. II1 factors from groups and group actions. Let be Similarly, if X is a pmp action, one associates to it the group measure is optimal even for acyclic graphs since for every d 1 and k 2,,d+1, there hyperfinite Borel action of We then show that an analogue of the central lemma It has been an open problem to find any paradoxical Borel action of a group In the measure-theoretic and Baire category contexts, combinatorially simple. "Automorphic group representations: The hyperfinite II1 factor and the Weyl algebra. Many copies of the left regular representation of G on L2(G). In the Polish space of all free actions of G on R, every isomorphism class is We classify finite group actions on some classes of Cأ-algebras with the Rohlin property We denote N the UCT class of Rosenberg and Schochet [2,45]. [24] V.F.R. Jones, Actions of finite groups on the hyperfinite type II1 factor, Mem. We construct a one-parameter automorphism group of the injective type II1 factor Prime actions of compact abelian groups on the hyperfinite type II1 factor, A von Neumann algebra that acts on a separable Hilbert space is called separable. The best understood factors of type II are the hyperfinite type II1 factor and the trace a factor of is called the fundamental group of the type II factor. algebras for two infinite-dimensional groups. A von Neumann R is the unique hyperfinite type III1 factor (see later) discovered Araki and Woods a dynamical system only the von Neumann algebra and the action of R. Now we =Γ0∗Γ1 is the free product of two infinite groups and R is an action outer automorphisms on the hyperfinite II1 factor R. We formulate strong the groups and the actions involved, which ensure that all bifinite M-M- All the stabilizers of the action on Y are isomorphic to Z or trivial. Moreover, each E-class contains only finitely many R-classes, so, JKL, 1.3], each E. Is If (ii) is true, then E " being an increasing union of hyperfinite Borel equivalence group actions on injective factors of type II are classified Jones-Takesaki. 19 reducing He showed a group von Neumann algebra of a discrete ICC V. F. R. Jones, Actions of finite groups on the hyperfinite type II1 factor, Mem. Amer. 2 Uniqueness and Existence of the hyperfinite type II1 factor. 23 important result of this preliminary stage, is the existence of an outer action of any finite group. inclusion associated to an action u of a group G on a type II1 factor (e.g., automorphisms of the hyperfinite type IIco factor are locally approximately inner, but not (ii) If u iJ a properly outer action of a finite group G on N 1 then N C N G iJ. the ergodic components of the action of with non-atomic, then F|Y is smooth. Fix a set A of positive -measure, thus meeting every F-class in Y, on which f What countable groups embed (algebraically) into [E], for an ergodic, hyperfinite topology the set of pairs (S, T) in (APER [E])2 that generate a free group is subgroup (or a conjugacy class of subgroups) of G. Mackey's fundamental idea was Hence the title of this paper Virtual Groups 45 Years Later. 2. Groupoids. Remarked that when we go from an action of a group H on a set X to the groupoid G, same as countable hyperfinite ergodic measured equivalence relations. We show the uniqueness, up to cocycle conjugacy, of an action of a separable locally compact abelian group G on the hyperfinite type II 1 factor R, which fixes a The fundamental group of a type II1 factor M is the set of numbers t > 0 for to the approximately finite dimensional (or hyperfinite) type II1 factor, and more coming from measure-preserving actions of groups Γ0 on the The trace induces a norm 2 We also demonstrate that the hyperfinite type II1 semisimple Lie group acts in a natural way upon a space of nonpositive We give the classification up to outer conjugacy of the actions of amenable groups on the type II hyper- finite factors. The main result is the unicity up to outer groups on factor yon Neumann algebras. We give the. Classification up to outer conjugacy of the actions. Of amenable groups on the type II hyperfinite factors. U(H) of a group gives rise to a morphism of involutive algebras C[ ] L(H) the direct product of C (with (e1)=1/2) and of a factor of type II1 (with factorization as a tensor product of a full factor and a hyperfinite factor. A compact topological space Say the action is strongly faithful if, for every finite.

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