On the structure of k-Lie algebras

TL;DR

This paper characterizes the structure constants of positive definite metric k-Lie algebras for k>3, showing they are sums of volume forms of orthogonal k-planes, extending previous results for k=3 and confirming a conjecture.

Contribution

It generalizes the structure of k-Lie algebras for k>3, providing a new geometric description and confirming a prior conjecture.

Findings

Structure constants are sums of volume forms of orthogonal k-planes.

Generalizes previous results for 3-Lie algebras.

Confirms a mathematical conjecture about k-Lie algebra structure.

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.