S-Expansion of Higher-Order Lie Algebras

By means of a generalization of the S-expansion method we construct a procedure to obtain expanded higher-order Lie algebras. It is shown that the direct product between an Abelian semigroup S and a higher-order Lie algebra ($\mathcal{G},[,\mathrm{.}\mathrm{.}\mathrm{.},])$ is also a higher-order Lie algebra. From this S-expanded Lie algebra are obtained resonant submultialgebras and reduced multialgebras of a resonant submultialgebra.