Generalized Lie triple derivations of Dihedron algebras

The purpose of this article is to determine the Lie triple derivations of the Dihedron algebras over any field F, (denoted by \(\mathfrak {M}\) $\mathfrak{M}$ ), and hence to obtain the alebra \(TDer(\mathfrak {M})\) $TDer(\mathfrak{M})$ of Lie triple derivations of \(\mathfrak {M}\) $\mathfrak{M}$ . Aside from Lie triple derivations of \(\mathfrak {M}\) $\mathfrak{M}$ we would also be able to extend the Lie triple derivations to generalized Lie triple derivations of this \(\mathfrak {M}\) $\mathfrak{M}$ . We would explicitly get a Lie triple derivation and generalized Lie triple derivation by means of its matrix representation.