2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66750We show that matrices in the same orbit of the SO(n, n|Z) action on the space of n\times n skew-symmetric matrices give strong Morita equivalent noncommutative tori, both at the C*-algebra level and at the smooth algebra level. This proves a conjecture of Rieffel and Schwarz.12 pages, minor improvements. To appear in J. Reine Angew. MathOperator AlgebrasQuantum Algebratext