An octonionic formulation of the M-theory algebra

摘要

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