Semi‐simple Extension of the (Super) Poincaré Algebra

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).

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