Free entropy dimension in amalgamated free products
نویسندگان
چکیده
منابع مشابه
Free Entropy Dimension in Amalgamated Free Products
We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some ‘exotic’ Popa algebra generators of free group factors are shown to have the expected free entropy dimension. We also show that microstates and non–microstates free entropy dimension agree f...
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SupposeM is a von Neumann algebra with normal, tracial state φ and {a1, . . . , an} is a set of self-adjoint elements in M. We provide an alternative uniform packing description of δ0(a1, . . . , an), the modified free entropy dimension of {a1, . . . , an}. For Arlan Ramsay In the attempt to understand the free group factors Voiculescu created a type of noncommutative probability theory. One fa...
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We prove a technical result, showing that the existence of a closable unbounded dual system in the sense of Voiculescu is equivalent to the finiteness of free Fisher information. This approach allows one to give a purely operatoralgebraic proof of the computation of the non-microstates free entropy dimension for generators of groups carried out in an earlier joint work with I. Mineyev [4]. The ...
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It is shown that the positive first-order theory of an HNN-extension G = 〈H, t; tat = φ(a)(a ∈ A)〉 can be reduced to the existential firstorder theory of G provided that A and B are proper subgroups of the base group H with A∩B finite. For an amalgamated free product G = H ∗A J , we show that the positive first-order theory of G can be reduced to the existential first-order theory of G in case ...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2008
ISSN: 0024-6115
DOI: 10.1112/plms/pdm054