On Invariants of m-Vector in Lorentzian Geometry

ÖREN İ.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.9, sa.1, ss.38-44, 2016 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 1
  • Basım Tarihi: 2016
  • Dergi Adı: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.38-44
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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).