An octonionic formulation of the M-theory algebra

Abstract

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.

References in corpus (2)

• Black Holes, Qubits and Octonions
• A magic pyramid of supergravities

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• The Magic Star of Exceptional Periodicity
• The Mile High Magic Pyramid
• Symmetrization of Jordan dialgebras
• Non-Associative Algebras and Quantum Physics -- A Historical Perspective
• Yang-Mills connections valued on the octonionic algebra
• Dirac and Maxwell systems in split octonions
• Clifford algebras, algebraic spinors, quantum information and applications
• Thermal Lie Superalgebras
• Octonionic D=11 Supergravity and 'Octavian Integers' as Dilaton Vectors