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

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

Abstract


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.


Keywords


Homogeneous Space; Lie Group Action; Orthogonal Matrix; Unit Sphere

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DOI: https://doi.org/10.37905/euler.v12i2.27752

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