MASAS AND BIMODULE DECOMPOSITIONS OF II1 FACTORS
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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A singular masa A in a II1 factor N is defined by the property that any unitary w ∈ N for which A = wAw∗ must lie in A. A strongly singular masa A is one that satisfies the inequality ‖EA − EwAw∗‖∞,2 ≥ ‖w − EA(w)‖2 for all unitaries w ∈ N , where EA is the conditional expectation of N onto A, and ‖ · ‖∞,2 is defined for bounded maps φ : N → N by sup{‖φ(x)‖2 : x ∈ N, ‖x‖ ≤ 1}. Strong singularity...
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The main result of this paper is the inequality d(u,N(A))/31 ≤ ‖EA − EuAu∗ ‖∞,2 ≤ 4d(u,N(A)), where A is a masa in a separably acting type II1 factor N , u ∈ N is a unitary, N(A) is the group of normalizing unitaries, d is the distance measured in the ‖ ·‖2-norm, and ‖ · ‖∞,2 is a norm defined on the space of bounded maps on N by ‖φ‖∞,2 = sup{‖φ(x)‖2 : ‖x‖ ≤ 1}. This result implies that a unita...
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.
متن کاملGenerators of II1 factors
In 2005, Shen introduced a new invariant, G(N), of a di use von Neumann algebra N with a xed faithful trace, and he used this invariant to give a uni ed approach to showing that large classes of II1 factors M are singly generated. This paper focuses on properties of this invariant. We relate G(M) to the number of self-adjoint generators of a II1 factor M : if G(M) < n/2, then M is generated by ...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2009
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/hap038