Classification of simple linearly compact n-Lie superalgebras

We classify simple linearly compact n-Lie superalgebras with n > 2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras of the form L = \oplus_{j=-1}^{n-1}L_j, where dim L_(n-1) = 1, L_(-1) and L_(n-1) generate L, and [L_(j), L_(n-j-1)] = 0 for all j, thereby reducing it to the known classification of simple linearly compact Lie superalgebras and their Z-gradings. The list consists of four examples, one of them being the n + 1-dimensional vector product n-Lie algebra, and the remaining three infinite-dimensional n-Lie algebras.