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We present a modified version of the definition of property RD for discretequantum groups given by Vergnioux in order to accommodate examples ofnon-unimodular quantum groups. Moreover we extend the construction of spectraltriples associated to discrete groups with length functions, originally due toConnes, to the setting of quantum groups. For quantum groups of rapid decay westudy the resulting spectral triples from the point of view of compact quantummetric spaces in the sense of Rieffel.

Compact quantum metric spaces from quantum groups of rapid decay