Quantum metrics from length functions on quantum groups
Operator Algebras
2025-11-10 v3 Quantum Algebra
Abstract
We study the quantum metric structure arising from length functions on quantum groups and show that for coamenable quantum groups of Kac type, the quantum metric information is captured by the algebra of central functions. Using this, we provide the first examples of length functions on (genuine) quantum groups which give rise to compact quantum metric spaces.
Keywords
Cite
@article{arxiv.2503.01501,
title = {Quantum metrics from length functions on quantum groups},
author = {Are Austad and David Kyed},
journal= {arXiv preprint arXiv:2503.01501},
year = {2025}
}
Comments
Minor changes and clarifications added. Accepted for publication in Journal of Functional Analysis