Continuous length functions on étale groupoids define quasi-Lip-norms whose state-space metrics become genuine metrics on each fibre of a transformation groupoid with rapid decay, and metrizing the weak*-topology when the unit space is finite.
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Metrics on $C^{\ast}$-algebras of \'Etale groupoids from length functions
Continuous length functions on étale groupoids define quasi-Lip-norms whose state-space metrics become genuine metrics on each fibre of a transformation groupoid with rapid decay, and metrizing the weak*-topology when the unit space is finite.