S-Expansion of Higher-Order Lie Algebras

TL;DR

This paper introduces a generalized S-expansion method to systematically construct and analyze expanded higher-order Lie algebras, including resonant submultialgebras and reductions, broadening algebraic tools for theoretical physics.

Contribution

It presents a novel generalization of the S-expansion technique specifically for higher-order Lie algebras, enabling new algebraic constructions and decompositions.

Findings

The direct product of an Abelian semigroup and a higher-order Lie algebra results in a higher-order Lie algebra.

The method allows the derivation of resonant submultialgebras from the expanded algebra.

Reduced multialgebras of resonant submultialgebras can be obtained through this procedure.

Abstract

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 ($\mathcal{G},[,...,])$ is also a higher-order Lie algebra. From this S-expanded Lie algebra are obtained resonant submultialgebras and reduced multialgebras of a resonant submultialgebra.