Recovering the Lie algebra from its extremal geometry

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  • Eindhoven University of Technology


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 simply-laced type, then L is a quotient of a Chevalley algebra of the same type.


Original languageEnglish
Pages (from-to)196-215
Number of pages20
JournalJournal of Algebra
Early online date25 Aug 2015
Publication statusPublished - 1 Nov 2015


  • Buildings, Lie algebras, Root groups, Shadow spaces

ASJC Scopus subject areas