Question: please help solve this. the question is complete. thank you. Find all derivations of the algebra of polynomials in z with complex coefficients C[z]. Show

please help solve this. the question is complete. thank you.

Find all derivations of the algebra of polynomials in z with complex coefficients C[z]. Show that the Lie algebra of derivations has a basis of elements Li, i 2 -1, i E Z such that [ Li, L;] = (i -j) Litj. Find all the ideals of this Lie algebra. (Hints: Find the eigenspaces of ad(Lo). Since ad(Lo) (I) C I, what can we conclude about eigenspaces of ad(Lo)?)

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