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arXiv · 2610.19791

Spectral truncations of SU(2) and the spectral localizer

Matt Verhoeven
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Abstract

We study operator systems arising from Peter-Weyl and Dirac spectral truncations of $\mathrm{SU}(2)$ 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 $\mathrm{prop} \leq 2$ 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 $\mathrm{SU}(2)$. 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 $κ\downarrow 0$.

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Matt Verhoeven. 2026-10-14. Spectral truncations of SU(2) and the spectral localizer. https://arxiv.org/abs/2610.19791

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