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...

-m,} each having multiplicity one. We now introduce the (quadratic) Casimir element, C {\displaystyle C} given by C = − ( u 1 2 + u 2 2 + u 3 2 ) {\displaystyle...

construction is the one in which x {\displaystyle x} is the (quadratic) Casimir element C {\displaystyle C} . In this case, π ( C ) = λ π I {\displaystyle...

_{k}\right)\;,} where summation over the eight indices k is implied. Casimir element Clebsch–Gordan coefficients for SU(3) Generalizations of Pauli matrices...

in the representation theory of Lie algebras. For example, a Casimir element is an element of such a center that is used to analyze Lie algebra representations...

the quadratic Casimir element of the universal enveloping algebra, and there is also a proof of the theorem that uses the Casimir element directly instead...

provide important information about the representations. The quadratic Casimir element is of particular importance in this regard. Although the canonical...

Representation of a Lie superalgebra Universal enveloping algebra Casimir element Infinitesimal character Harish-Chandra homomorphism Fundamental representation...

is compact and simple of rank 1, and so it has a single independent Casimir element, a quadratic invariant function of the three generators which commutes...

Casimir I the Restorer (Polish: Kazimierz I Odnowiciel; 25 July 1016 – 19 March 1058), a member of the Piast dynasty, was the duke of Poland from 1040...