Proper Moufang sets with abelian root groups are special

Segev, Yoav

doi:10.1090/S0894-0347-09-00631-6

Proper Moufang sets with abelian root groups are special
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by Yoav Segev

J. Amer. Math. Soc. 22 (2009), 889-908

DOI: https://doi.org/10.1090/S0894-0347-09-00631-6

Published electronically: January 5, 2009

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Abstract:

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.

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