Let I be a differential system on a manifold M. The infinitesimal symmetry algebra of I is the set of all vectors fields X on M such that preserve I. In this worksheet we present an example, due to E. Cartan of a rank 7 Pfaffian system on a 15-dimensional manifold whose infinitesimal symmetry algebra is the split real form of the exceptional Lie algebra f4 .
Anderson, Ian M., "A Rank 7 Pfaffian System on a 15-Dimensional Manifold with f4 Symmetry Algebra" (2015). Tutorials on... in 1 hour or less. Paper 4.