2011/02/25 by Hailing Li, Ying Wang · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Finite Group Theory Research
paper · doi:10.1080/03081080903350153
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. Keywords: generalized Lie triple derivationBorel subalgebramaximal nilpotent subalgebrablock diagonal maphomothetyAMS Subject Classifications: 17B2017B40 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.