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.

A tensor extension of the Poincaré algebra are proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension are also found in the dimensions D = 2, 3, 4.

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Abstract. We consider the introduction of gauge fields and the Higgs effect for Goldstone particles with spin 1/2 Higgs and others (Higgs (1966), Migdal and Polyakov (1966), Kibble (1967)) have noted that when interactions are turned on between Goldstone particles and gauge fields, the Goldstone particles vanish and those gauge fields whose quantum numbers coincide with the quantum numbers of the Goldstone particles acquire mass (the Higgs effect). We consider in this article a variant of the Higgs effect, in which the "absorption" of the Goldstone particles is effected by a "foreign" gauge field, i.e., by a gauge fields whose quantum numbers differ from those of the Goldstone particles.We consider as the symmetry group G the direct product of a Poincare group with a certain group of internal symmetry, supplemented by the following transformations:We use the definitions of Volkov and Akulov (1973). The spontaneous violation of the considered symmetry group under the assumption that the direct product of the Poincare group and of the internalsymmetry group leaves the vacuum invariant, leads to the appearance of Goldstone particle with spin 1/2/ ( Volkov and Akulov (1972), Volkov and Akulov (1973)).Let us consider the gauge transformations of the group G with parameters l, u, t, and ~, which depend on xv and gauge fields that are coefficient functions of the differentials dxv and de of the differential form A(d) with the following transformation law:A'(d) =

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