| Résume | In 2013 Hawkins, Skalski, White and Zacharias constructed and investigated spectral triples on crossed product C*-algebras by actions of discrete groups which are in a natural sense equicontinuous. Following Connes, one of the ingedients of their construction are certain multiplication operators associated with length functions on the group. In their article they further formulated the question for whether their triples turn the corresponding crossed product C*-algebras into compact quantum metric spaces. The aim of this talk is to give a gentle introduction into Rieffel's theory of compact quantum metric spaces. By combining his ideas on horofunction boundaries of groups with results from metric geometry, I will further answer the question of Hawkins, Skalski, White and Zacharias in the affirmative in the case of virtually abelian groups, equipped with suitable length functions. |
