Nilpotent subalgebras of semisimple Lie algebras

Levy, Paul and McNinch, George and Testerman, Donna (2009) Nilpotent subalgebras of semisimple Lie algebras. Comptes Rendus Mathématique, 347 (9-10). pp. 477-482.

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.