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arXiv · 2609.37761

Spectral gap, internality of relative commutants, and non-hyperlinear groups

Vadim Alekseev·Jihao Liu·Andreas Thom
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Abstract

We prove that the relative commutant of a finite unitary tuple in a tracial matrix ultraproduct is internal whenever its conjugation operator has a spectral gap off the commutant. This implies the existence of a non-hyperlinear group.

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Vadim Alekseev, Jihao Liu, Andreas Thom. 2026-09-29. Spectral gap, internality of relative commutants, and non-hyperlinear groups. https://arxiv.org/abs/2609.37761

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