2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58582We calculate twisted denominator identities of the fake monster superalgebra and use them to construct new examples of supersymmetric generalized Kac-Moody superalgebras. Their denominator identities give new infinite product identities.13 pages, latex2e, some details addedQuantum Algebratext