Models of the real forms.

We shall now assume the following result from the classification of simple Lie algebras over https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756478/4cadc9cc-32ae-4840-8f83-07e1ed499955/content/pg118_10.tif"/> . The number of isomorphism classes of the various exceptional types 119are as follows: G₂: 2, F₄: 3, E₆: 5, E₇: 4, E_g: 3. For each type we have given the corresponding number of simple Lie algebras with different signatures for the Killing forms. Hence we have obtained models (representatives) for every isomorphism class. It is clear also that two algebras of the same type and signature are isomorphic. We summarize our results in the following table: