Representation theory of Lie groups | Lie algebras

Casimir element

In mathematics, a Casimir element (also known as a Casimir invariant or Casimir operator) is a distinguished element of the center of the universal enveloping algebra of a Lie algebra. A prototypical example is the squared angular momentum operator, which is a Casimir element of the three-dimensional rotation group. The Casimir element is named after Hendrik Casimir, who identified them in his description of rigid body dynamics in 1931. (Wikipedia).

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Related pages

Group representation | Lie group | Pauli matrices | Quantum number | Simple Lie algebra | Center (ring theory) | Topological quantum number | Pauli–Lubanski pseudovector | Homogeneous polynomial | Rigid body dynamics | Kronecker delta | Clebsch–Gordan coefficients | Semisimple Lie algebra | Spin (physics) | Lie algebra representation | Fredholm theory | Structure constants | Lie group action | Harish-Chandra isomorphism | Mathematics | Fermion | Riemannian manifold | Euclidean space | Lie algebra | Pseudo-differential operator | Weyl's theorem on complete reducibility | Basis (linear algebra) | Bilinear form | Universal enveloping algebra | Laplace–Beltrami operator | Symmetric algebra | Irreducible representation | Angular momentum operator | Killing form