J. Aust. Math. Soc.  74 (2003), 313-330
The Wielandt subalgebra of a Lie algebra

Donald W. Barnes
  1 Little Wonga Rd
  Cremorne NSW 2090
Daniel Groves
  Department of Mathematics
  School of Advanced Studies
  Australian National University
  ACT 0200
  Current address:
  Mathematical Institute
  24--29 St. Giles
  Oxford, OX1 3LB

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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