# Oksana Yakimova (Friedrich-Schiller-University Jena)

## Symmetric invariants and polynomial rings.

For a reductive Lie algebra $$\mathfrak{g}$$ of rank r, the ring of symmetric invariants $$S(\mathfrak{g})^\mathfrak{g}$$ is a polynomial ring in r variables. We will discuss the importance of this property and then describe some other (non-reductive) Lie algebras having it.