Questions tagged [casimir-element]

$\DeclareMathOperator\ad{ad}\DeclareMathOperator\Tr{Tr}$I have been thinking about this for some time but have had no luck. I have found some sources that say higher Casimir elements can be obtained ...

Given a general Lie algebra, is there a general procedure to find all its Casimir operator?

I am looking for a complete description (if possible with proof) of the Casimir operators (i.e., generators and relations for the center of the universal enveloping algebra) for the Jacobi Lie algebra ...

Let $G$ be a compact Lie group (not necessarily connected) and $\rho:G\to \mathrm{End}(V)$ an irreducible (hence finite-dimensional) unitary representation of $G$. Let $\mathfrak{g}$ be the Lie ...

I am interested in explicit formulae for the Casimir elements (or "Casimir operators") of low-dimensional, real, non-Abelian Lie algebras (d=2,3, and possibly 4). I am wondering if there is any ...