2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74467Following the approach to pseudo-Riemannian symmetric spaces developed in math.DG/0408249 we exhibit examples of indefinite hyper-Kaehler symmetric spaces with non-abelian holonomy. Moreover, we classify indecomposable hyper-Kaehler symmetric spaces whose metric has signature (4,4n). Such spaces exist if and only if n=0,1,3.20 pagesDifferential GeometryRepresentation Theory53C26; 53C35text