An octonionic formulation of the M-theory algebra

A. Anastasiou, L. Borsten, M. J. Duff, L. J. Hughes, S. Nagy

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We give an octonionic formulation of the N = 1 supersymmetry algebra in D = 11, including all brane charges. We write this in terms of a novel outer product, which takes a pair of elements of the division algebra A and returns a real linear operator on A. More generally, with this product comes the power to rewrite any linear operation on ℝn (n = 1, 2, 4, 8) in terms of multiplication in the n-dimensional division algebra 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.

Original languageEnglish
Article number22
JournalJournal of High Energy Physics (JHEP)
Issue number11
Publication statusPublished - Nov 2014


  • Extended Supersymmetry
  • M-Theory


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