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arXiv · 2110.03076

Hyperlinear approximations to amenable groups come from sofic approximations

Peter Burton
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Abstract

We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, showing that every hyperlinear approximation to such a group is essentially produced from a sofic approximation. This translates to a quantitative relationship between Hilbert-Schmidt and permutation stability for approximate homomorphisms which appropriately separate the elements of the group.

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Peter Burton. 2021-10-06. Hyperlinear approximations to amenable groups come from sofic approximations. https://arxiv.org/abs/2110.03076

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