Nilpotent subalgebras of semisimple Lie algebras

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 ill any Borel subalgebra of g. To cite this article: P Levy et al., C R. Acad. Sci. Paris, Ser. 1347 (2009). (C) 2009 Published by Elsevier Masson SAS on behalf of Academie des sciences.


Published in:
Comptes Rendus Mathematique, 347, 477-482
Year:
2009
Keywords:
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 Record created 2010-11-30, last modified 2018-09-13


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