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Abstract
Let be a complex semisimple Lie algebra,
be a Borel subalgebra of
and
denote the maximal nilpotent subalgebra of
. In this article, we prove that every generalized Lie triple derivation of
can be written as the sum of a Lie triple derivation and a block diagonal map. We also show that every generalized Lie triple derivation for
of each classical complex simple Lie algebra is the sum of a Lie triple derivation and a homothety.
Acknowledgements
The authors thank the anonymous referee and Prof C.-K. Li for their helpful comments. Also, they would like to thank the referee for showing them a simplification in the proof of Lemma 3.2.