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arXiv · 2008.02700

Inner ideals and structurable algebras: Moufang sets, triangles and hexagons

Tom De Medts·Jeroen Meulewaeter
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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 $D \oplus D$ 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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Tom De Medts, Jeroen Meulewaeter. 2020-08-06. Inner ideals and structurable algebras: Moufang sets, triangles and hexagons. https://arxiv.org/abs/2008.02700

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