2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/189808It is shown that the Lie group of invertible elements of the quaternion algebra carries a family of natural closed Friedmann-Lemaitre-Robertson-Walker metrics.A slightly more technical version of "Natural geometry of nonzero quaternions" IJTP 46 (2) (2007) 251-257Mathematical PhysicsAstrophysicsGeneral Relativity and Quantum Cosmology53C50 (Primary), 53B30, 22E30, 53B50 (Secondary)text