Metric Lie n-algebras and double extensions

Abstract

We prove a structure theorem for Lie n-algebras possessing an invariant inner product. We define the notion of a double extension of a metric Lie n-algebra by another Lie n-algebra and prove that all metric Lie n-algebras are obtained from the simple and one-dimensional ones by iterating the operations of orthogonal direct sum and double extension.

10 pages

References in corpus (7)

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• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Pluecker-type relations for orthogonal planes
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• Topological branes, p-algebras and generalized Nahm equations
• $w_{\infty }$ 3-algebra
• Towards Holographic Gravity Dual of N=1Superconformal Chern-Simons Gauge Theory
• Nambu Bracket for M Theory
• Three lectures on 3-algebras
• Quadratic $n$-ary Hom-Nambu algebras
• Classification of $(n+3)$-dimensional metric $n$-Lie algebras
• (p+1)-Algebra for Super p-Brane: the Nambu Bracket Reformulation
• Metric $n$-Lie Algebras