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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 simply-laced type, then L is a quotient of a Chevalley algebra of the same type.
Original language | English |
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Pages (from-to) | 196-215 |
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
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Lie Algebras and incidence geometry
Shpectorov, S. (Principal Investigator) & Gramlich, R. (Co-Investigator)
Engineering & Physical Science Research Council
1/09/09 → 31/05/10
Project: Research Councils