| For a Lie algebra g of type B, D, E or F, we can apply a grading g = g -2⊕ g -1⊕ g 0⊕ g 1⊕ g 2 and then define a quartic form and a skew-symmetric bilinear form on g 1, thereby constructing a Freudenthal triple system. The structure of the Freudenthal triple system is examined using root system methods available in the Lie algebra context. In the important cases g = E8 and g = D4, we determine the groups stabilizing the quartic form and both the quartic and bilinear forms. |
