J. Aust. Math. Soc.
74 (2003), 313330

The Wielandt subalgebra of a Lie algebra



Daniel Groves
Department of Mathematics
School of Advanced Studies
Australian National University
ACT 0200
Australia
Current address:
Mathematical Institute
2429 St. Giles
Oxford, OX1 3LB
UK
grovesd@maths.ox.ac.uk



Abstract

Following the analogy with group theory, we
define the Wielandt subalgebra of a
finitedimensional Lie algebra to be the
intersection of the normalisers of the subnormal
subalgebras. In a nonzero algebra,this is a
nonzero ideal if the ground field has
characteristic 0 or if the derived algebra is
nilpotent, allowing the definition of the
Wielandt series. For a Lie algebra with
nilpotent derived algebra, we obtain a bound for
the derived length in terms of the Wielandt
length and show this bound to be best possible.
We also characterise the Lie algebras with
nilpotent derived algebra and Wielandt length 2.

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