AbilinearformfonanonassociativetriplesystemTissaidtobeinvariantifandonlyiff(,d)=f(a,)=f(c,)foralla,b,c,d∈T.(T,f)iscalledapseudo-metrictriplesystemiffisnon-degenerateandinvariant.Adecompositiontheoryfortriplesystemsandpseudo-metrictriplesystemsisestablished.Moreover,thefinite-dimensionalmetricLietriplesystemsarecharacterizedintermsofthestructureofthenon-degenerate,invariantandsymmetricbilinearformsonthem.
