2010/04/19 by D. Soroka, Dmitrij V. Soroka, Soroka, Dmitrij V. +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1004.3194
LaTeX, 11 pages. Some specification and a reference are added
openalex publication_date 2010/04/19 · arxiv created 2011/07/31 · arxiv updated 2011/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A semi-simple tensor extension of the Poincaré algebra is given for the arbitrary dimensions D. It is illustrated 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 o(N) generalization of this extension is introduced in the D=4 dimensions. It is established that this generalization is a direct sum of the 4-dimensional Lorentz algebra so(3,1) and orthosymplectic algebra osp(N,4) (super-AdS algebra). Quadratic Casimir operators for the generalization are constructed. The form of these operators indicates that the components of an irreducible representation for this generalization are distinguished by the mass, angular momentum and quantum numbers corresponding to the internal symmetry, tensor and supersymmetry generators. That generalizes the Regge trajectory idea. The probable unification of the N=10 supergravity with the SO(10) GUT model is discussed. This paper is dedicated to the memory of Anna Yakovlevna Gelyukh.