Abstract

We present a nonlinear realization of the 5-graded Lie algebra associated to a Kantor triple system. Any simple Lie algebra can be realized in this way, starting from an arbitrary 5-grading. In particular, we get a unified realization of the exceptional Lie algebras f4,e6,e7,e8, in which they are respectively related to the division algebras R,C,H,O.

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