Casimir goes to Casimir
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In mathematics, "Casimir goes to Casimir" is an aphorism expressing the centrality and universality of the Casimir operator. This can be summarized as follows:
Given any representation V of a semisimple Lie algbera 
, the Casimir operator induces a -module homomorphism Ω of V (as follows from the centrality of the Casimir operator). Let now V1,V2 be two representations of with corresponding Casimir operators Ω1,Ω2, and 
a -module homomorphism. Then since Ω is a member of the universal enveloping algebra, it commutes with f, i.e. 
. Stated less rigorously, Casimir goes to Casimir under any -module homomorphism.
