Limits of Jordan Lie subalgebras

2015/08/19 by Saito, Mutsumi
#17B20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1508.04508

Abstract

Let g be a simple Lie algebra of rank n over C. We show that the n-dimensional abelian ideals of a Borel subalgebra of g are limits of Jordan Lie subalgebras. Combining this with a classical result by Kostant, we show that the g-module spanned by all n-dimensional abelian Lie subalgebras of g is actually spanned by the Jordan Lie subalgebras.

Related

• Abelian ideals with given dimension in Borel subalgebras
• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra
• Abelian ideals of a Borel subalgebra and root systems
• Abelian ideals of maximal dimension for solvable Lie algebras
• Locally simple subalgebras of diagonal Lie algebras