Explicit Computation of Lie algebra invariants
The ring of polynomial invariants of a Lie algebra carries important information concerning the representations of the algebra. Furthermore, it is also isomorphic, over an algebraically closed field of characteristic zero, to the center of the universal enveloping algebra. In this talk, I will present some practical methods for the computation of the ring of polynomial invariants and also of the field of rational invariants. These methods are implemented in the computational algebra package SageMath and can be used to compute invariants of solvable Lie algebras. The presentation is based on joint work with Igor Martins Silva.