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...
متن کاملAmenable Actions of Amalgamated Free Products
We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
متن کاملPositive theories of HNN-extensions and amalgamated free products
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 ...
متن کامل2 00 9 Amenable actions of amalgamated free products
We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.
متن کاملExactness of Reduced Amalgamated Free Product C {algebras
Some completely positive maps on reduced amalgamated free products of C∗–algebras are constructed, showing that every reduced amalgamated free product of exact C∗–algebras is exact. Consequently, every amalgamated free product of exact discrete groups is exact.
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 2009
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091506001556