2014/10/22 by Hans Cuypers, Cuypers, Hans, Kieran Roberts +3
Mathematics · #17B20 #51E24 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA) #math.CO #math.RA #msc:17B20 #msc:51E24
paper · pdf · doi:10.48550/arxiv.1410.5937
24 pages
arxiv created 2014/10/22 · arxiv updated 2014/10/23
An element x of a Lie algebra L over the field F is extremal if [x,[x,L]]=Fx. Under minor assumptions, it is known that, for a simple Lie algebra L, the extremal geometry \calE(L) is a subspace of the projective geometry of L and either has no lines or is the root shadow space of an irreducible spherical building Δ. We prove that if Δ is of simply-laced type, then L is a quotient of a Chevalley algebra of the same type.