I have this definition of the Casimir element from Knapp p.294 $$ \Omega= {\sum} B\left(X_{i},X_{j}\right)\widetilde{X}_{i}\widetilde{X}_{j}. $$ The prrof that Knapp does for the Casimir element being in the center of U(g) is a little bit cumbersome using a previus lemma etc. All other books I know do a simple proof but based on another definition. Does anybody see a short way with few lines to proof the centrality of the Casimir element starting from this definition? By the way... does anybody know why Knapp use this definition of the Casimir element? Thanks in advance
2026-05-15 05:08:56.1778821736
How to proof the Casimir element is in the Center of U(g)
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