The nil radical for Lie or anti-Lie triple systems (Q1801902)

The author introduces and investigates a nil radical (the maximal nilpotent ideal) for Lie and anti-Lie triple systems. The notion of powers of an ideal introduced here is not the straightforward generalization of the Lie algebra case one might expect, and therefore the ensuring notion of nilpotency is stronger than for Lie algebras. The following seems to provide a counterexample to Theorem 7 (which states that \([R,T,T]\subset N\) for the Lister solvable radical \(R\) and the nilradical \(N\) of the Lie triple system \(T\)): Let \(L\) be a semisimple Lie algebra, \(M\) an irreducible \(L\)-module and \(T\) the Lie triple system built from the split null extension \(L+M\). Then \(R=M\), \(N=0\) (by the author's definition) yet \([R,T,T]=R\).