Semi-Simple Extension of the (Super)‎ Poincaré Algebra

الملخص EN

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).