  Let $q$ be an algebraic Lie algebra and $q<m>$ a (generalised) Takiff
algebra. Any finite order automorphism $\theta$ of $q$ induces an automorphisms
of $q<m>$ of the same order, denoted $\Theta$. We study invariant-theoretic
properties of representations of the fixed point subalgebra of $\Theta$ on
other eigenspaces of $\Theta$ in $q<m>$.
