Lie n superderivations and generalized Lie n superderivations of superalgebras

Abstract

In the paper, we study Lie n superderivations and generalized Lie n superderivations of superalgebras, using the theory of functional identities in superalgebras. We prove that if A = A0 ⊕ A1 is a prime superalgebra with deg(A1) ≥ 2n + 5, n ≥ 2, then any Lie n superderivation of A is the sum of a superderivation and a linear mapping, and any generalized Lie n superderivation of A is the sum of a generalized superderivation and a linear mapping.

Keywords

• lie n superderivation
• generalized lie n superderivation
• superalgebra
• functional identity
• 17a70
• 16w10
• 16w55