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=\oplus_{j=-1}^{n-1} L_j, such that L_{-1}=g, 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.

Final version to appear in Communications in Mathematical Physics

References in corpus (1)

• Three lectures on 3-algebras

Cited by in corpus (17)

• n-ary algebras: a review with applications
• Generalized derivations of (color) n-ary algebras
• Super $w_{\infty }$ 3-algebra
• Generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras
• Classification of linearly compact simple Nambu-Poisson algebras
• Degenerations of Filippov algebras
• 3-ary Hom-Lie superalgebras induced Hom-Lie superalgebras
• Contractions of Filippov algebras
• $3$-BiHom-Lie superalgebras induced by BiHom-Lie superalgebras
• Topics on n-ary algebras
• Split Regular $Hom$-Leibniz Color $3$-Algebras
• $n$-Ary generalized Lie-type color algebras admitting a quasi-multiplicative basis
• (p,q)-deformed Virasoro-Witt n-algebra
• Split 3-Lie-Rinehart color algebras
• $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras
• Quadratic and symplectic structures on 3-(Hom)-$\rho$-Lie algebras
• Commutative $n$-ary superalgebras with an invariant skew-symmetric form