Classification of simple linearly compact n-Lie superalgebras

Abstract

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=n−1j=−1Lj, 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.