ON INVARIANTS OF CONTINUOUS SUBGROUPS OF THE GENERALIZED POINCARÉ GROUP P (1, 4)

V. FEDORCHUK

Pedagogical Academy, Institute of Mathematics,

Podchora̧żych 2, 30-084, Kraków, Poland

Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, National Ukrainian Academy of Sciences, Naukova 3b, 79-053, L’viv, Ukraine

Abstract

For all continuous subgroups of the group P (1, 4) the invariants in the fivedimensional Minkowski space M(1, 4) have been constructed. The invariants obtained are one-, two-, three and four-dimensional.

On the base of the invariants obtained the nonsingular manifolds in the spaces M(1, 3) × R and M(1, 4) × R invariant under nonconjugate subgroups of the group P(1,4) have been described.

The manifolds obtained have already been used for the symmetry reduction of some important equations of the theoretical physics in the spaces M(1, 3)×R and M(1, 4) × R.