The following lemma is an easy consequence of Chevalley's

The following lemma is an easy consequence of Chevalley's construction. Lemma 1. The Lie algebra generated by e;J;, i = 0, ... , n - 1, ~'and the relations

C§(A) has the following rootspace decomposition C§(A) = L(B C§,.,

(ii) ( ·, ·) extends in a unique way to a nondegenerate invariant symmetric bilinear form on CS(A), called the standard invariant form, or Killing form.