Inner ideals and structurable algebras: Moufang sets, triangles and hexagons
Abstract
We construct Moufang sets, Moufang triangles and Moufang hexagons using inner ideals of Lie algebras obtained from structurable algebras via the Tits--Kantor--Koecher construction. The three different types of structurable algebras we use are, respectively: (1) structurable division algebras, (2) algebras D D for some alternative division algebra D, equipped with the exchange involution, (3) matrix structurable algebras M(J,1) for some cubic Jordan division algebra J. In each case, we also determine the root groups directly in terms of the structurable algebra.
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