Questions tagged [casimir-element]
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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 ...
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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 ...
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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 ...
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What is the cubic Casimir element of $\mathfrak{sl}_3$?
$\DeclareMathOperator\ad{ad}\DeclareMathOperator\Tr{Tr}$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 ...
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How to find Casimir operators?
Given a general Lie algebra, is there a general procedure to find all its Casimir operator?
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