A group with at least subexponential hyperlinear profile

2018/06/13 by William Slofstra, Slofstra, William · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Markov Chains and Monte Carlo Methods #Operator Algebras (math.OA) #Quantum Physics (quant-ph) #math.GR #math.OA #quant-ph

paper · pdf · doi:10.48550/arxiv.1806.05267

13 pages

arxiv created 2018/06/13 · openalex publication_date 2018/06/13 · arxiv updated 2018/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The hyperlinear profile of a group measures the growth rate of the dimension of unitary approximations to the group. We construct a finitely-presented group whose hyperlinear profile is at least subexponential, i.e. at least exp(1/ε^k) for some 0 < k < 1. We use this group to give an example of a two-player non-local game requiring subexponential Hilbert space dimension to play near-perfectly.

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