Semi-simple extension of the (Super) Poincaré algebra. (English) Zbl 1216.81088
Summary: A semi-simple tensor extension of the Poincaré algebra is proposed for the arbitrary dimensions \(D\). It is established that this extension is a direct sum of the \(D\)-dimensional Lorentz algebra so(\(D - 1\), 1) and \(D\)-dimensional anti-de Sitter (AdS) algebra so(\(D - 1\), 2). A supersymmetric also semi-simple generalization of this extension is constructed in the \(D=4\) dimensions. It is shown that this generalization is a direct sum of the 4-dimensional Lorentz algebra so(3, 1) and orthosymplectic algebra osp(1, 4) (super-AdS algebra).
MSC:
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 81Q60 | Supersymmetry and quantum mechanics |
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
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