Gromov-Hausdorff Convergence of Spectral Truncations for Quantum Groups
Operator Algebras
2026-05-01 v1
Abstract
We study the quantum Gromov-Hausdorff convergence of spectral truncations for compact quantum groups. Using a proper length function, we define a Dirac operator and the associated spectral truncations. This work extends the previous convergence results for tori (Leimbach-van Suijlekom) to a broad class of quantum groups, and provides the first Gromov-Hausdorff convergence result for spectral truncations on quantum groups, encompassing both compact and discrete quantum groups. Our results are applicable to , and discrete quantum groups with strong polynomial growth.
Keywords
Cite
@article{arxiv.2604.27475,
title = {Gromov-Hausdorff Convergence of Spectral Truncations for Quantum Groups},
author = {Xintao Peng and Qin Wang},
journal= {arXiv preprint arXiv:2604.27475},
year = {2026}
}