Inner ideals and structurable algebras: Moufang sets, triangles and hexagons
arXiv:2008.02700
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 for some alternative division algebra , equipped with the exchange involution, (3) matrix structurable algebras for some cubic Jordan division algebra . In each case, we also determine the root groups directly in terms of the structurable algebra.
36 pages