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Nilpotent subalgebras of semisimple Lie algebras

Research output: Contribution to journalJournal article

Published

Journal publication date05/2009
JournalComptes Rendus Mathématique
Journal number9-10
Volume347
Number of pages6
Pages477-482
Original languageEnglish

Abstract

Let g be the Lie algebra of a semisimple linear algebraic group. Under mild conditions on the characteristic of the underlying field, one can show that any subalgebra of g consisting of nilpotent elements is contained in some Borel subalgebra. In this Note, we provide examples for each semisimple group G and for each of the torsion primes for G of nil subalgebras not lying in any Borel subalgebra of g.