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Journal of Lie Theory 27 (2017), No. 1, 051--084
Copyright Heldermann Verlag 2017

Limits of Jordan Lie Subalgebras

Mutsumi Saito
Dept. of Mathematics, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan

Let g be a simple Lie algebra of rank n over the complex numbers 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.

Keywords: Cartan subalgebra, Jordan Lie subalgebra.

MSC: 17B20

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