English

Spectral continuity for \'etale groupoids with the Rapid decay property

Operator Algebras 2025-09-30 v1

Abstract

We show that the reduced groupoid C*-algebras of continuous fields of \'etale groupoids satisfying the rapid decay property yield continuous fields of C*-algebras. This establishes a new sufficient criterion that applies in the non-amenable case where the full and reduced groupoid algebras may differ. Potential applications include convergence of spectra in inverse systems of finite-index subgroups and magnetic models on hyperbolic lattices.

Keywords

Cite

@article{arxiv.2509.24145,
  title  = {Spectral continuity for \'etale groupoids with the Rapid decay property},
  author = {Tom Stoiber},
  journal= {arXiv preprint arXiv:2509.24145},
  year   = {2025}
}