Convergence of Fourier truncations for compact quantum groups and finitely generated groups

Abstract

We generalize the Fejér-Riesz operator systems defined for the circle group by Connes and van Suijlekom to the setting of compact matrix quantum groups and their ergodic actions on C*-algebras. These truncations form filtrations of the containing C*-algebra. We show that when they and the containing C*-algebra are equipped with suitable quantum metrics, then under suitable conditions they converge to the containing C*-algebra for quantum Gromov-Hausdorff distance. Among other examples, our results are applicable to the quantum groups $S{U}_q(2)$ and their homogeneous spaces $S_q^2$.

21 pages; v2 Many small improvements. No change in conclusions; v3 several references added, various minor improvements, renumbered sections. No change in conclusions

References in corpus (8)

• Spectral truncations in noncommutative geometry and operator systems
• The Podles spheres converge to the sphere
• Truncated Geometry on the Circle
• Dirac operators for matrix algebras converging to coadjoint orbits
• Tolerance Relations and Quantization
• Berezin Quantization From Ergodic Actions of Compact Quantum Groups, and Quantum Gromov-Hausdorff Distance
• Modular spectral triples and deformed Fredholm modules
• The Gauge Group and Perturbation Semigroup of an Operator System

Cited by in corpus (1)

• A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity