2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163404We prove a structure theorem for Lie n-algebras possessing an invariant inner product. We define the notion of a double extension of a metric Lie n-algebra by another Lie n-algebra and prove that all metric Lie n-algebras are obtained from the simple and one-dimensional ones by iterating the operations of orthogonal direct sum and double extension.10 pagesRepresentation TheoryHigh Energy Physics - TheoryRings and Algebrastext