2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158022In arXiv:math/0603621 we introduced the notion of a partial translation $C^*$-algebra for a discrete metric space. Here we demonstrate that several important classical $C^*$-algebras and extensions arise naturally by considering partial translation algebras associated with subspaces of trees.13 pagesOperator AlgebrasMetric Geometry46L05, 47L80text