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

Autor:	De Medts, Tom, Meulewaeter, Jeroen
Rok vydání:	2020
Předmět:	Mathematics - Rings and Algebras Mathematics - Group Theory 17A30 17B45 17B60 17B70 51E24 16W10 17C40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 36 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.02700 Zobrazit plný text záznamu View this record from Arxiv