## Classification of simple linearly compact n-Lie superalgebras

##### Author(s)

Cantarini, Nicoletta; Kac, Victor
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Show full item record##### 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.

##### Date issued

2010-04##### Department

Massachusetts Institute of Technology. Department of Mathematics##### Journal

Communications in Mathematical Physics

##### Publisher

Springer-Verlag

##### Citation

Cantarini, Nicoletta, and Victor G. Kac. “Classification of Simple Linearly Compact n-Lie Superalgebras.” Communications in Mathematical Physics 298.3 (2010): 833–853. Web.

Version: Author's final manuscript

##### ISSN

0010-3616

1432-0916