I need to solve two assignments in Lie algebras. These assignments are not very difficult, but my knowledges in Lie algebras aren't good.
1. Let be a derivation of the Lie algebra . Show that if commutes with every inner derivation, then ()C(), where C() denotes the centre of .
2. Let x gl(n,F) have n distinct eigenvalues 1..n in F. Prove that eigenvalues of ad are the n scalars - (1i,jn)
Your prompt reply will be highly appreciated