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Abstract
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 E(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 simplylaced type, then L is a quotient of a Chevalley algebra of the same type.
Original language  English 

Pages (fromto)  196215 
Number of pages  20 
Journal  Journal of Algebra 
Volume  441 
Early online date  25 Aug 2015 
DOIs  
Publication status  Published  1 Nov 2015 
Keywords
 Buildings
 Lie algebras
 Root groups
 Shadow spaces
ASJC Scopus subject areas
 Algebra and Number Theory
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Dive into the research topics of 'Recovering the Lie algebra from its extremal geometry'. Together they form a unique fingerprint.Projects
 1 Finished

Lie Algebras and incidence geometry
Shpectorov, S. & Gramlich, R.
Engineering & Physical Science Research Council
1/09/09 → 31/05/10
Project: Research Councils