Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space

Khadjiev D., Gőksal Y.

Advances in Applied Clifford Algebras, vol.26, no.2, pp.645-668, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1007/s00006-015-0627-9
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.645-668
  • Keywords: Hyperbolic geometry, Hyperbolic number, Invariant
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Let E12 be the real 2-dimensional pseudo-Euclidean space of index 1, O(1; 1) be the group of all pseudo-orthogonal transformations of E12 and SO(1; 1) = {g ∈ O(1; 1) : det g = 1}. In the present paper, complete systems of invariants of m-tuples in E12 for these groups and complete systems of relations between elements of the complete systems of invariants are obtained. For solutions of the these problems, hyperbolic numbers are used.