Invariants of semisimple Lie algebras acting on associative algebras

If ${\mathfrak g}$ is a Lie algebra of derivations of an associative algebra $R$, then the subalgebra of invariants is the set $R^{\mathfrak g} = \{ r \in R \mid \delta(r) = 0 \text{ for all } \delta \in {\mathfrak g}\}.$ In this paper, we study the relationship between the structure of $R^{\mathfrak g}$ and the structure of $R$, where $\mathfrak g$ is a finite dimensional semisimple Lie algebra over a field of characteristic zero acting finitely on $R$, when $R$ is semiprime.