An octonionic formulation of the M-theory algebra

Understand

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 R^n (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.