PreprintCC BY-SA 4.0arXiv
Spectral gap, internality of relative commutants, and non-hyperlinear groups
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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BibTeX
@misc{alekseev2026spectral,
title = {{Spectral gap, internality of relative commutants, and non-hyperlinear groups}},
author = {Vadim Alekseev and Jihao Liu and Andreas Thom},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.37761},
eprint = {2609.37761},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37761},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Spectral gap, internality of relative commutants, and non-hyperlinear groups
AU - Vadim Alekseev
AU - Jihao Liu
AU - Andreas Thom
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.37761
UR - https://arxiv.org/abs/2609.37761
AB - 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.
ER -