Considerations on Super Poincare Algebras and their Extensions to Simple Superalgebras

Details Considerations on Super Poincare Algebras and their Extensions to Simple Superalgebras Considerations on Super Poincare Algebras and their Extensions to Simple Superalgebras

2001-12-19

arxiv.org/abs/hep-th/0112177v2

Rev.Math.Phys. 14 (2002) 519-530

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, AMS-LaTeX. Version to appear in the Reviews in Mathematical Physics

Scientific paper

10.1142/S0129055X0200134X

We consider simple superalgebras which are a supersymmetric extension of $\fspin(s,t)$ in the cases where the number of odd generators does not exceed 64. All of them contain a super Poincar\'e algebra as a contraction and another as a subalgebra. Because of the contraction property, some of these algebras can be interpreted as de Sitter or anti de Sitter superalgebras. However, the number of odd generators present in the contraction is not always minimal due to the different splitting properties of the spinor representations under a subalgebra. We consider the general case, with arbitrary dimension and signature, and examine in detail particular examples with physical implications in dimensions $d=10$ and $d=4$.

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