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=j=-1n-1 Lj, such that L-1=g, where dim Ln-1=1, L-1 and Ln-1 generate L, and [Lj, Ln-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.
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