The S-expansion method is a generalization of the Inönü-Wigner (IW) contraction that allows
to study new non-trivial relations between different Lie algebras. Basically, this method
combines a Lie algebra G with a finite abelian semigroup S in such a way that a new S-
expanded algebra GS can be defined. When the semigroup has a zero-element and/or a
specific decomposition, which is said to be resonant with the subspace structure of the
original algebra, then it is possible to extract smaller algebras from GS which have …

… To answer this one should consider the complete family of abelian semigrops, ie, to take
into account the history of their classification: … to represent any semigroup and Lie algebra
by means of their respective selectors and structure constants 5. to perform all possible S-expansions
(GxS, resonant subalgebra, reduced algebra, reduction of the resonant subalgebra) of a
given Lie algebra. …