Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-04-16
JHEP 0805:054,2008
Physics
High Energy Physics
High Energy Physics - Theory
8 pages, minor changes, published version
Scientific paper
10.1088/1126-6708/2008/05/054
We find that the structure constants 4-form of a metric 3-Lie algebra is the sum of the volume forms of orthogonal 4-planes proving a conjecture in math/0211170. In particular, there is no metric 3-Lie algebra associated to a $\mathfrak{u}(N)$ Lie algebra for $N>2$. We examine the implication of this result on the existence of a multiple M2-brane theory based on metric 3-Lie algebras.
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