Abstract
We give an octonionic formulation of the \( \mathcal{N}=1 \) supersymmetry algebra in D = 11, including all brane charges. We write this interms of a novel outer product, which takes a pair of elements of the division algebra \( \mathbb{A} \) and returns a real linear operator on \( \mathbb{A} \). More generally, with this product comes the power to rewrite any linear operation on \( {\mathbb{R}}^n \) (n =1, 2, 4, 8) in terms of multiplication in the n-dimensional division algebra \( \mathbb{A} \). Finally, we consider the reinterpretation of the D =11 supersymmetry algebra as an octonionic algebra in D =4 and the truncation to division subalgebras.
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Anastasiou, A., Borsten, L., Duff, M.J. et al. An octonionic formulation of the M-theory algebra. J. High Energ. Phys. 2014, 22 (2014). https://doi.org/10.1007/JHEP11(2014)022
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DOI: https://doi.org/10.1007/JHEP11(2014)022