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Nilpotent subalgebras of semisimple Lie algebras

Research output: Contribution to journalJournal article

Published

<mark>Journal publication date</mark>05/2009
<mark>Journal</mark>Comptes Rendus Mathématique
Issue9-10
Volume347
Number of pages6
Pages477-482
<mark>Original language</mark>English

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.