English

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 SU(N)SU(N),SO(N)SO(N) 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}
}