Let A be a finite dimensional
algebra over a field F of characteristic zero and let L be a completely reducible Lie
algebra of derivations of A. If A is associative, then there exists an L-invariant
Wedderburn factor of A. If A is a Lie algebra, there exists an L-invariant Levi factor
of A. If A is a solvable Lie algebra, lhere exists an L-invariant Cartan subalgebra of
A. This paper deals with the uniqueness of such L-invariant subalgebras. For the
associative case the assumption of characteristic zero can be dropped if we assume
that the radical of A is L-invariant.
