It is well-known that the nilradical of a finite-dimensional Lie algebra over a field of characteristic p is not necessarily characteristic (that is, not invariant under all derivations of the algebra). But is there a solvable Lie algebra whose nilradical is not characteristic?
Dera David,
ln New Year issue of the journal Linear Algebra and its Applications (vol. 488. 1.01.2016) appeared an article about some solvable Lie algebras you could be interested in (pp.135-147).
Greetings, Tadeusz
Thank you Tadeusz. That article deals with Lie algebras over the real and complex fields, and so the nilradical will always be characteristic. Nevertheless, it is an interesting paper which I hadn't seen before.
By a result of Maksimenko such an example would need a nilradical of nilpotency class greater than or equal to p-1, where p is the characteristic of the underlying field. So such an example may be easiest to construct over a field of small characteristic.
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