  Lie algebras endowed with an action by automorphisms of any of the symmetric
groups S3 or S4 are considered, and their decomposition into a direct sum of
irreducible modules for the given action is studied.
  In case of S3-symmetry, the Lie algebras are coordinatized by some
nonassociative systems, which are termed generalized Malcev algebras, as they
extend the classical Malcev algebras. These systems are endowed with a binary
and a ternary products, and include both the Malcev algebras and the Jordan
triple systems.
