Generalized symmetries and deformations of the direct sums of Lie algebras

Abstract

The problem of the combined space-time and internal symmetry of elementary Particles is investigated from the view-point of the Lie algebras deformation theory. It is demonstrated that the deformations of the direct sum of the Poincaré and internal symmetry algebras conserve the structure of the direct sum, if the internal symmetry is semi-simple or is described by the special type of algebras with abelian ideal. So the internal and space-time characteristics of the system remain independent.