Question: Let L be a Lie ajgehra ever a eld IF and let H be a subspace of L (net necessarily a suhalgehraU. We then dene

Let L be a Lie ajgehra ever a eld IF and let H be a subspace of L (net necessarily a suhalgehraU. We then dene the normaliser H; {H} cf H in L to he the space HL(H}:={1 E L | [1,19] g H}. We dene the centraliser CL(H) cfH in L In bethe space cam := [1: EL | [1,H]={I}. Exercise: Use the Jacchi identity to she-v.1.r that bath the nennaliser and the centraliser are Lie suh algebras of L

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