
Journal of Lie Theory 27 (2017), No. 1, 051084 Copyright Heldermann Verlag 2017 Limits of Jordan Lie Subalgebras Mutsumi Saito Dept. of Mathematics, Graduate School of Science, Hokkaido University, Sapporo 0600810, Japan saito@math.sci.hokudai.ac.jp Let g be a simple Lie algebra of rank n over the complex numbers C. We show that the ndimensional 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 gmodule spanned by all ndimensional abelian Lie subalgebras of g is actually spanned by the Jordan Lie subalgebras. Keywords: Cartan subalgebra, Jordan Lie subalgebra. MSC: 17B20 [ Fulltextpdf (417 KB)] for subscribers only. 