Questions tagged [casimir]

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List of Casimir elements of low dimensional Lie algebras

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 ...
4
votes
1answer
500 views

The Casimir invariant of an irreducible representation of a compact Lie group

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 ...
2
votes
1answer
116 views

Casimir operators for Jacobi Lie algebra

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 ...