Lie triple systems arose initially in Cartan’s study of Riemannian geometry. Jacobson [8] first introduced them in connection with problems from Jordan theory and quantum mechanics, viewing Lie triple systems as subspaces of Lie algebras that are closely related to the ternary product. Lister gave the structure theory of Lie triple systems of characteristic 0 in [14]. Hopkin introduced the concepts of nilpotent ideals and the nil-radical of Lie triple systems, she k https://www.iomcworld.org/ generalized Engel’s theorem to Lie triple systems in characteristic zero