J. Aust. Math. Soc.
74 (2003), 313-330
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The Wielandt subalgebra of a Lie algebra
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Daniel Groves
Department of Mathematics
School of Advanced Studies
Australian National University
ACT 0200
Australia
Current address:
Mathematical Institute
24--29 St. Giles
Oxford, OX1 3LB
UK
grovesd@maths.ox.ac.uk
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Abstract
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Following the analogy with group theory, we
define the Wielandt subalgebra of a
finite-dimensional Lie algebra to be the
intersection of the normalisers of the subnormal
subalgebras. In a non-zero algebra,this is a
non-zero 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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