2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/50117For Connes' spectral triples, the group of automorphisms lifted to the Hilbert space is defined and used to fluctuate the metric. A few commutative examples are presented including Chamseddine and Connes' spectral unification of gravity and electromagnetism. One almost commutative example is treated: the full standard model. Here the lifted automorphisms explain O'Raifeartaigh's reduction $SU(2)\times U(3)/\zz_2.$25 pages LaTeX, 1 figure, this paper will not be submitted to any journal, in particular not to Nucl.Phys.BHigh Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext