Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators

R. Campoamor-Stursberg, S. G. Low

Given a semidirect product $\mathfrak{g}=\mathfrak{s}\uplus \mathfrak{r}$ of semisimple Lie algebras $\mathfrak{s}$ and solvable algebras $\mathfrak{r}$, we construct polynomial operators in the envelo…