I have started learning Lie algebra and I can't understand one example given in the notes.
Given:
[h_{\alpha},e_{\alpha}] = 2 e_{\alpha}
[h_{\alpha},f_{\alpha}] = -2 f_{\alpha}
[e_{\alpha},f_{\alpha}] = h_{\alpha}
and that
[x,y] = K(x,y) t_{\alpha}
if \alpha is a root and x \in...