2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59342We show that the skew-symmetrized product on every Leibniz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative multiplication on E which, when E is a Lie algebra, is derived from the integrated adjoint representation. We apply this construction to realize the bracket operations on the sections of Courant algebroids and on the ``omni-Lie algebras'' recently introduced by the second author.24 pages. Version 2 has minor correctionsDifferential GeometryQuantum Algebra17A32, 53C20, 20N05text