Applications of Hyperbolic Numbers to the Invariant Theory in Two-Dimensional Pseudo-Euclidean Space

Abstract

Let be the real 2-dimensional pseudo-Euclidean space of index 1, O(1; 1) be the group of all pseudo-orthogonal transformations of and SO(1; 1) = {g a O(1; 1) : det g = 1}. In the present paper, complete systems of invariants of m-tuples in 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.