N-Lie Algebra (?)(n,1)

Much more interest has been shown in the study of n-Lie algebras since 1985, when Filippov first introduced the concept. In this paper, we define a new n-Lie algebras on a divided power algebra (?)(n,1) over a field F with char F= p> 3. We determine the generators and all derivations of (?)(n,1) as n-Lie algebras. Meanwhile, we also construct a class of nilpotent subalgebras of (?)(n,1) as n-Lie algebras.