Octonionic Realizations of 1-dimensional Extended Supersymmetries. A Classification

Abstract

The classification of the octonionic realizations of the one-dimensional extended supersymmetries is here furnished. These are non-associative realizations which, albeit inequivalent, are put in correspondence with a subclass of the already classified associative representations for 1D extended supersymmetries. Examples of dynamical systems invariant under octonionic realizations of the extended supersymmetries are given. We cite among the others the octonionic spinning particles, the N=8 KdV, etc. Possible applications to supersymmetric systems arising from dimensional reduction of the octonionic superstring and M-theory are mentioned.

12 pages, LaTex

References in corpus (5)

• On the Classification of N-extended Supersymmetric Quantum Mechanical Systems
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• Generalized Space-time Supersymmetries, Division Algebras and Octonionic M-theory
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Cited by in corpus (7)

• Quaternionic and Octonionic Spinors. A Classification
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• Weaving Worldsheet Supermultiplets from the Worldlines Within
• The Real Anatomy of Complex Linear Superfields
• On Clifford-Algebraic "Holoraumy", Dimensional Extension, and SUSY Holography
• Hermitian versus holomorphic complex and quaternionic generalized supersymmetries of the M-theory. A classification
• On the Construction and the Structure of Off-Shell Supermultiplet Quotients