The Orthogonal Matrices of O(2) under A Transitive Standard Action of S^1

Kurniadi, Edi
Pratiwi, Putri Nisa
Queency, Aurillya
Parmikanti, Kankan

Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi
Volume 12 Issue 2 December 2024

In this paper, we study a Lie group action of the matrix Lie group O(2) on S1 the unit sphere  . The research aims to establish the explicit formulas for all entries of  whose action on S1  is transitive. All possibilities matrices of  are given in which the space  is homogeneous. We prove that there are exactly two matrices in  such that  is the homogeneous space. Moreover, the homogeneous spaces  S(n-1) of O(n)   for n=3  are also discussed.