Geodesic
Proper Moufang sets with abelian root groups are special
Segev, Yoav1
1 Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel
Journal of the American Mathematical Society, Tome 22 (2009) no. 3, pp. 889-908

Voir la notice de l'article provenant de la source American Mathematical Society

Moufang sets are split $BN$-pairs of rank one, or the Moufang buildings of rank one. As such they have been studied extensively, being the basic ‘building blocks’ of all split $BN$-pairs. A Moufang set is proper if it is not sharply $2$-transitive. We prove that a proper Moufang set whose root groups are abelian is special. This resolves an important conjecture in the area of Moufang sets. It enables us to apply the theory of quadratic Jordan division algebras to such Moufang sets.
DOI : 10.1090/S0894-0347-09-00631-6

Segev, Yoav 1

1 Department of Mathematics, Ben-Gurion University, Beer-Sheva 84105, Israel 
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Segev, Yoav. Proper Moufang sets with abelian root groups are special. Journal of the American Mathematical Society, Tome 22 (2009) no. 3, pp. 889-908. doi: 10.1090/S0894-0347-09-00631-6

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