1
$\begingroup$

Let L be a finite-dimensional complex semisimple lie algebra, then ad(L)=Der(L). (Der is short for derivation). In order to show that ad(L)=Der(L), the book says that it only need to show that the prependicular space to ad(L) is zero. This is where I don't quite understand. The book I am reading is Introduction to Lie Algebras by Karin Erdmann, and the proof is on page 85. I am sorry that I cannot find a link for this book.

  • 0
    The proof in this book on page $85$ says much more; in fact it is more detailed than the answers below.2016-09-14

2 Answers 2