On λ-k-skew Lie product involving commuting additive maps on prime ∗-algebras.

Let be an ∗-algebra and k ∈ ℤ + . For A , B ∈ , the product defined by ∗ [ A , δ A (B) λ ∗ ] k = ∗ [ A , ∗ [ A , δ A (B) λ ∗ ] k − 1 ] 1 , where ∗ [ A , δ A (B) λ ∗ ] 0 = δ A (B) λ ∗ and ∗ [ A , δ A (B) λ ∗ ] 1 = A δ A (B) λ ∗ − δ A (B) λ ∗ A ∗ , is called λ - k -skew Lie product of A and B , where δ A (B) λ ∗ = A B − λ B A ∗ . This paper discusses some useful characteristics of λ - k -skew Lie products on prime ∗-algebras. Moreover, we investigate the effects of an additive map ϕ on with a λ - k -skew Lie product. [ABSTRACT FROM AUTHOR]