Classification of Simple Linearly Compact n-Lie Superalgebras
By N. Cantarini, V. Kac. 2009
66 citations recorded by the source corpus.
We classify simple linearly compact n-Lie superalgebras with n > 2 over a field $${\mathbb{F}}$$ of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive $${\mathbb{Z}}$$-graded Lie superalgebras of the form $${L=\oplus_{j=-1}^{n-1} L_j}$$, 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 $${\mathbb{Z}}$$-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.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/fd718e73b9748aed44925c9f523c87ff2cf851a3
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Citations in the corpus
- n-ary algebras: a review with applications (2010, background): “It has recently been shown [178] that the class of simple linearly compact n-Lie algebras contains four types for n > 2, the An+1 FAs (called O n in [178]) plus three infinite-dimensional n-Lie algebras.”