The connection of (split-)division algebras with Clifford algebras andsupersymmetry is investigated. At first we introduce the class of superalgebrasconstructed from any given (split-)division algebra. We further specify whichreal Clifford algebras and real fundamental spinors can be reexpressed in termsof split-quaternions. Finally, we construct generalized supersymmetriesadmitting bosonic tensorial central charges in terms of (split-)divisionalgebras. In particular we prove that split-octonions allow to introduce asplit-octonionic M-algebra which extends to the (6,5) signature the propertiesof the 11-dimensional octonionic M-algebras (which only exist in the (10,1)Minkowskian and (2,9) signatures).
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