On the fundamental group of type II1 factors
نویسندگان
چکیده
منابع مشابه
On the fundamental group of type II1 factors.
We present here a shorter version of the proof of our earlier work, showing that the von Neumann factor associated with the group Z(2)SL(2,Z) has trivial fundamental group.
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In the context of Free Probability Theory, we study two different constructions that provide new examples of factors of type II1 with prescribed fundamental group. First we investigate state-preserving group actions on the almost periodic free Araki-Woods factors satisfying both a condition of mixing and a condition of free malleability in the sense of Popa. Typical examples are given by the fr...
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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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Recently, Boutonnet, Chifan, and Ioana proved that McDuff’s family of continuum many pairwise nonisomorphic separable II1 factors are in fact pairwise non-elementarily equivalent by proving that any ultrapowers of two distinct members of the family are nonsiomorphic. We use Ehrenfeucht-Fraisse games to provide an upper bound on the quantifier-depth of sentences which distinguish these theories.
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In the paper, we study the generator problem of type II1 factors. By defining a new concept closely related to the numbers of generators of a von Neumann algebra, we are able to show that a large class of type II1 factors are singly generated, i.e., generated by two self-adjoint elements. In particular, we show that most of type II1 factors, whose free entropy dimensions are known to be less th...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 2004
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.2333960100