## A Division Algebra Classification of Generalized Supersymmetries |

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abelian tensorial central algebra structure analytic continuation anticommutators antisymmetric tensors antisymmetrized products bosonic components entering bosonic sector bosonic tensorial central Brasileiro de Pesquisas Centro Brasileiro charge conjugation matrix classification of Clifford Clifford algebras complex and quaternionic complex holomorphic supersymmetry complex or quaternionic complex spinors constraint D-dimensional denoted dimensional reduction division-algebra constrained eleven-dimensional M-algebra entering the hermitian entering the symmetric Euclidean fundamental spinors given space-time hermitian and holomorphic hermitian matrix hermitian supersymmetry HLS scheme Hodge duality identically equal investigation irreducible representations Lorentz M-theory matrix Zab maximal number metries Minkowskian n-component number of bosonic number of real octonionic q mod Qa,Qb quaternionic spacetimes quaternionic spinors quaternionic supersymmetry rank-A real counting real numbers real spinors realizing the Clifford respectively restricted Rio de Janeiro saturated bosonic signatures subalgebras super superconformal algebras based supersym supersymmetry algebra symmetric matrix tensorial central charges time-like total number totally antisymmetric Weyl projected Xavier Sigaud