On the structure of k-Lie algebras

Abstract

We show that the structure constants of $k$-Lie algebras, $k>3$, with a positive definite metric are the sum of the volume forms of orthogonal $k$-planes. This generalizes the result for $k=3$ in arXiv:0804.2662 and arXiv:0804.3078, and confirms a conjecture in math/0211170.

4 pages, minor changes and a reference added

References in corpus (4)

• Comments on the Bagger-Lambert theory and multiple M2-branes
• Membranes on an Orbifold
• Multiple M2-branes and the Embedding Tensor
• Aspects of Multiple Membranes

Cited by in corpus (9)

• Multiple M2-branes and Generalized 3-Lie algebras
• One-loop corrections to Bagger-Lambert theory
• An N=1 Superfield Action for M2 branes
• Multiple Membranes from Gauged Supergravity
• Janus field theories from multiple M2 branes
• Coulomb Branch of the Lorentzian Three Algebra Theory
• A note on Quantum Aspects of Multiple Membranes
• Metric Lie n-algebras and double extensions
• On Nambu-Lie 3-algebra representations