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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.

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Definition

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Symmetric invariant tensors of simple Lie algebras

Examples

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Casimir element

Nodes70
Edges69
Triples21
Avg. degree1.97
Density0.028571
Components1

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Casimir element

Top relations

related to Casimir elements and representation theory · 8
Casimir element → By, By Racah's, By Schur's Lemma, Casimir, Laplacian, Lie, The, The Casimir
related to Relation to the Laplacian on G · 6
Casimir element → Casimir, If, Laplacian, Lie, Riemannian, Then
related to Uniqueness of the quadratic Casimir element · 5
Casimir element → Casimir, For, Killing, Lie, Since
related to Symmetric invariant tensors of simple Lie algebras · 2
Casimir element → Casimir, Constructing

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Important terminology

displaystyle casimir algebra invariant lie element mathfrak representation symmetric universal enveloping elements tensors form basis group operator center also given

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Casimir elementrelated to Casimir elements and representation theoryBy Racah's0.60section
Casimir elementrelated to Casimir elements and representation theoryLie0.60section
Casimir elementrelated to Casimir elements and representation theoryThe Casimir0.60section
Casimir elementrelated to Casimir elements and representation theoryLaplacian0.60section
Casimir elementrelated to Casimir elements and representation theoryBy0.60section
Casimir elementrelated to Casimir elements and representation theoryBy Schur's Lemma0.60section
Casimir elementrelated to Casimir elements and representation theoryCasimir0.60section
Casimir elementrelated to Casimir elements and representation theoryThe0.60section
Casimir elementrelated to Relation to the Laplacian on GIf0.60section
Casimir elementrelated to Relation to the Laplacian on GLie0.60section
Casimir elementrelated to Relation to the Laplacian on GRiemannian0.60section
Casimir elementrelated to Relation to the Laplacian on GThen0.60section

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