Analysis reveals quantum metric information captured by central functions in coamenable quantum groups, suggesting new compact quantum metrics.
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.
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Austad et al. (2025) studied this question.
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