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Hyperplane section $${\mathbb {O}\mathbb {P}}^2_0$$ of the complex Cayley plane as the homogeneous space $${\text F}_4/{\text P}_4$$. (English) Zbl 1249.32019
The authors present a transitive action of the exceptional complex Lie group $$F_4$$ on the hyperplane section of the complex Cayley plane $${\mathbb {O}\mathbb {P}}^2$$. Clifford algebras, spin groups and the representation theory are used.
##### MSC:
 32M12 Almost homogeneous manifolds and spaces 14M17 Homogeneous spaces and generalizations
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