1
$\begingroup$

If $\alpha$ is a root, then the only multiples of α which are roots are $\alpha, -\alpha, 0$. Here $\alpha$ is a root of a simple lie algebra. How do I prove this?

1 Answers 1

1

An argument showing this is given on page 38 of Humphreys' Introduction to Lie Algebras and Representation Theory, #9 in Springer GTM series. It is based on knowledge of $sl_2$-theory and some other basic properties.

  • 0
    hey, thanx, but is there any other way of proving it. I am reading semi simple lie algebras and representations by cahn, and have not covered sl2 theory.2012-03-06