Type II1 factors satisfying the spatial isomorphism conjecture
نویسندگان
چکیده
conjecture Jan Cameron ∗, Erik Christensen †, Allan M. Sinclair ‡,Roger R. Smith §,Stuart White ¶,Alan D. Wiggins ‖ ∗Department of Mathematics, Vassar College, Poughkeepsie, NY 12604, U.S.A.,†Institute for Mathematiske Fag, University of Copenhagen, Copenhagen, Denmark.,‡School of Mathematics, University of Edinburgh, JCMB, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, Scotland.,§Department of Mathematics, Texas A&M University, College Station, TX 77843, U.S.A.,¶School of Mathematics and Statistics, University of Glasgow, University Gardens, Glasgow Q12 8QW, Scotland., and ‖Department of Mathematics
منابع مشابه
On a Class of Type Ii1 Factors with Betti Numbers Invariants
We prove that a type II1 factor M can have at most one Cartan subalgebra A satisfying a combination of rigidity and compact approximation properties. We use this result to show that within the class HT of factors M having such Cartan subalgebras A ⊂ M , the Betti numbers of the standard equivalence relation associated with A ⊂ M ([G2]), are in fact isomorphism invariants for the factorsM , β HT...
متن کاملThe classification problem for von Neumann factors
We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 ≤ λ ≤ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the isomorphism relation of type II1 factors is not smooth. We also prove that the isomorphism relation for von Neumann II1 factors is analytic, but is not Borel.
متن کاملA Note on the Classification of Gamma Factors
One of the earliest invariants introduced in the study of finite von Neumann algebras is the property Gamma of Murray and von Neumann. The set of separable II1 factors can be split in two disjoint subsets: those that have the property Gamma and those that do not have it, called full factors by Connes. In this note we prove that it is not possible to classify separable II1 factors satisfying the...
متن کاملSTRONG RIGIDITY OF II1 FACTORS ARISING FROM MALLEABLE ACTIONS OF w-RIGID GROUPS, II
We prove that any isomorphism θ : M0 ≃ M of group measure space II1 factors, M0 = L∞(X0, μ0)⋊σ0 G0, M = L ∞(X,μ)⋊σ G, with G0 containing infinite normal subgroups with the relative property (T) of Kazhdan-Margulis (i.e. G0 w-rigid) and G an ICC group acting by Bernoulli shifts σ, essentially comes from an isomorphism of probability spaces which conjugates the actions with respect to some identi...
متن کاملA Kurosh Type Theorem for Type Ii1 Factors
The classification of type II1 factors (of discrete groups) was initiated by Murray and von Neumann [MvN] who distinguished the hyperfinite type II1 factor R from the group factor LFr of the free group Fr on r ≥ 2 generators. Thirty years later, Connes [Co2] proved uniqueness of the injective type II1 factor. Thus, the group factor LΓ of an ICC amenable group Γ is isomorphic to the hyperfinite ...
متن کامل