Semi-simple $o(N)$-extended super-Poincaré algebra

Abstract

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.

LaTeX, 11 pages. Some specification and a reference are added

References in corpus (9)

• Maxwell Superalgebra and Superparticle in Constant Gauge Backgrounds
• Generalized cosmological term from Maxwell symmetries
• Tensor extension of the Poincaré algebra
• Deforming the Maxwell-Sim Algebra
• AdS--Maxwell superalgebra and supergravity
• Deformed Maxwell Algebras and their Realizations
• Multiplet containing components with different masses
• Generalized Wigner-Inonu Contractions and Maxwell (Super)Algebras
• Multiplet with components of different masses

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