Lie triple derivations of dihedron algebra - Arshad, Minahal; Munir, Muhammad Mobeen (Frontiers in Physics, 2023)
Let K be a 2-torsion free unital ring and D(K) is Dihedron algebra over K. In the present article, we prove that every Lie triple derivation of D(K) can be written as sum of Lie triple derivation of K, Jordan triple derivation of K and some inner derivation of D. We also prove that a generalized Lie triple derivation : D(K) → D(K) associated with the Lie triple derivation h : D(K) → D(K) exists iff can be represented in the form (τ ) = h(τ ) + λτ where λ lies in the center of D(K). We finally conclude that to obtain complete algebra of Lie triple derivation and generalized Lie triple of D(K) , we first need to find Lie triple derivation and Jordan triple derivation of K.