A class of II1 factors with many non conjugate Cartan subalgebras
نویسندگان
چکیده
منابع مشابه
Cartan Subalgebras and Bimodule Decompositions of Ii1 Factors
Let A ⊂M be a MASA in a II1 factor M. We describe the von Neumann subalgebra of M generated by A and its normalizer N (A) as the set Nw q (A) consisting of those elements m ∈M for which the bimodule AmA is discrete. We prove that two MASAs A and B are conjugate by a unitary u ∈ Nw q (A) iff A is discrete over B and B is discrete over A in the sense defined by Feldman and Moore [5]. As a consequ...
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In this paper we consider two von Neumann subalgebras B0 and B of a type II1 factor N . For a map φ on N , we define ‖φ‖∞,2 = sup{‖φ(x)‖2 : ‖x‖ ≤ 1}, and we measure the distance between B0 and B by the quantity ‖EB0 −EB‖∞,2. Under the hypothesis that the relative commutant in N of each algebra is equal to its center, we prove that close subalgebras have large compressions which are spatially is...
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This is a continuation of our previous paper studying the structure of Cartan subalgebras of von Neumann factors of type II1. We provide more examples of II1 factors having either zero, one or several Cartan subalgebras. We also prove a rigidity result for some group measure space II1 factors.
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We prove that the normalizer of any diffuse amenable subalgebra of a free group factor L(Fr) generates an amenable von Neumann subalgebra. Moreover, any II1 factor of the form Q ⊗̄L(Fr), with Q an arbitrary subfactor of a tensor product of free group factors, has no Cartan subalgebras. We also prove that if a free ergodic measure preserving action of a free group Fr, 2 ≤ r ≤ ∞, on a probability ...
متن کاملHochschild Cohomology of Ii1 Factors with Cartan Masas
In this paper we prove that for a type II1 factor N with a Cartan maximal abelian subalgebra (masa), the Hochschild cohomology groups Hn(N, N)=0, for all n ≥ 1. This generalizes the result of Sinclair and Smith, who proved this for all N having separable predual.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2012
ISSN: 0001-8708
DOI: 10.1016/j.aim.2012.07.004