On Invariants of m-Vector in Lorentzian Geometry


ÖREN İ.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, vol.9, no.1, pp.38-44, 2016 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 1
  • Publication Date: 2016
  • Title of Journal : INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Page Numbers: pp.38-44

Abstract

Let G be the group M(n, 1) generated by all pseudo-orthogonal transformations and translations of Lorentzian space E-1(n) or G = SM(n, 1) is the subgroup of M(n, 1) generated by rotations and translations of E-1(n). We describe the correlations between Gram determinant detG(x(1),..., x(m)) of the system {x(1),..., x(m)} and the number of linearly independent null vectors in the system {x(1),..., x(m)}. Using methods of invariant theory and these results, the system of generators of the polynomial ring of all G-invariant polynomial functions of vectors x(1), x(2),..., x(m) in E-1(n) is obtained for groups G = M(n, 1) and G = SM(n, 1).