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Geometries from inner ideals of structurable algebras De, Tom


In our earlier study of low rank geometries related to exceptional groups, it became clear that structurable algebras play an important role. The natural question arose to what extent it would be possible to recover those geometries directly from the structurable algebras and their associated Tits-Kantor-Koecher Lie algebra. It turns out that the notion of an inner ideal is essential. We have been able to recover many geometries of rank one and two directly from the algebras in a surprisingly direct fashion. This is related to the geometries of extremal elements studied intensively by Arjeh Cohen and his collaborators, but our approach allows for many more geometries.

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