nLab Casimir operator

Definition

Given a Lie algebra $\mathfrak{g}$, then a Casimir element or Casimir invariant is an element in the center of its universal enveloping algebra $U(\mathfrak{g})$.

Often this is considered with some Lie algebra representation in mind, in which case one speaks of Casimir operators.

References

Named after Hendrik Casimir, who discovered the concept in the context of rigid body dynamics.

• Wikipedia, Casimir element