Advances in High Energy Physics
Volume 2009 (2009), Article ID 234147, 9 pages
doi:10.1155/2009/234147
Research Article

Semi-Simple Extension of the (Super) Poincaré Algebra

Dmitrij V. Soroka and Vyacheslav A. Soroka

Kharkov Institute of Physics and Technology, 1, Akademicheskaya St., 61108 Kharkov, Ukraine

Received 7 January 2009; Accepted 11 March 2009

Academic Editor: Kingman Cheung

Copyright © 2009 Dmitrij V. Soroka and Vyacheslav A. Soroka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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).