Division Algebras, Extended Supersymmetries and Applications

Abstract

I present here some new results which make explicit the role of the division algebras R,C,H,O in the construction and classification of, respectively, N=1,2,4,8 global supersymmetric quantum mechanical and classical dynamical systems. In particular an N=8 Malcev superaffine algebra is introduced and its relation to the non-associative N=8 SCA is discussed. A list of present and possible future applications is given.

8 pages, LaTex (Elsevier style); to appear in Nucl. Phys. B Proc. Suppl. Contribution to the proceedings of the conference "Supersymmetry and Quantum Field Theory", Kharkov, July 2000

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