PreprintCC BY 4.0arXiv
Spectral truncations of SU(2) and the spectral localizer
Abstract
We study operator systems arising from Peter-Weyl and Dirac spectral truncations of SU(2) in the sense of Connes-Van Suijlekom. We determine operator system invariants for these systems, including the C*-envelope and uniform bounds on the propagation number. For Peter-Weyl truncations, we find prop ≤ 2 for all connected compact Lie groups, generalizing known results for the torus. We also carry out an analysis of the spectral localizer by Loring and Schulz-Baldes on SU(2). In this analysis, we find numerical evidence that an index map for operator systems previously proposed by Van Suijlekom only captures the right information in a suitable interval of the parameter κ, instead of the limit κ↓ 0.
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BibTeX
@misc{verhoeven2026spectral,
title = {{Spectral truncations of SU(2) and the spectral localizer}},
author = {Matt Verhoeven},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19791},
eprint = {2610.19791},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19791},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral truncations of SU(2) and the spectral localizer
AU - Matt Verhoeven
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19791
UR - https://arxiv.org/abs/2610.19791
AB - We study operator systems arising from Peter-Weyl and Dirac spectral truncations of SU(2) in the sense of Connes-Van Suijlekom. We determine operator system invariants for these systems, including the C^*-envelope and uniform bounds on the propagation number. For Peter-Weyl truncations, we find prop ≤ 2 for all connected compact Lie groups, generalizing known results for the torus. We also carry out an analysis of the spectral localizer by Loring and Schulz-Baldes on SU(2). In this analysis, we find numerical evidence that an index map for operator systems previously proposed by Van Suijlekom only captures the right information in a suitable interval of the parameter κ, instead of the limit κ↓ 0.
ER -