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Lie algebras endowed with an action by automorphisms of any of the symmetricgroups S3 or S4 are considered, and their decomposition into a direct sum ofirreducible modules for the given action is studied.  In case of S3-symmetry, the Lie algebras are coordinatized by somenonassociative systems, which are termed generalized Malcev algebras, as theyextend the classical Malcev algebras. These systems are endowed with a binaryand a ternary products, and include both the Malcev algebras and the Jordantriple systems.

Lie algebras with S3 or S4-action, and generalized Malcev algebras