Question: please help solve this. (1) Let L be a Lie algebra and let C(L) be the centre of L. Show that an equality dim L/C(L)

please help solve this.

(1) Let L be a Lie algebra and let C(L) be the centre of L. Show that an equality dim L/C(L) = 1 is impossible. (2) Show that for any positive integer n, gIn(C) can be written as a direct sum of two ideals, one of which is 5L1(C)

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