T∗-extension of Lie triple systems

In this paper, we introduce the notion of T∗-extension of a Lie triple system. Then we show that T∗-extension is compatible with nilpotency, solvability, and it preserves in certain sense the decomposition properties. In addition, we investigate the equivalence of T∗-extensions using cohomology. Finally, we show that every finite-dimensional nilpotent metrised Lie triple system over an algebraically closed field is the T∗-extension of an appropriate quotient system.