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All Journal Jambura Journal of Mathematics Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi
Queency, Aurillya
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Computer Science & IT Mathematics

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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
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v12i2.27752

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.
Struktur Simplektik pada Aljabar Lie Affine aff(2,R) Queency, Aurillya; Kurniadi, Edi; Firdaniza, Firdaniza
Jambura Journal of Mathematics Vol 6, No 1: February 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v6i1.23254

Abstract

In this research, we studied the affine Lie algebra aff(2,R). The aim of this research is to determine the 1-form in affine Lie algebra aff(2,R) which is associated with its symplectic structure so that affine Lie algebra aff(2,R) is a Frobenius Lie algebra. Realized the elements of the affine Lie algebra aff(2,R) in matrix form, then calculated the Lie brackets and formed the structure matrix of the affine Lie algebra aff(2,R). 1-form of the affine Lie algebra aff(2,R) is obtained from the determinant of the structure matrix of the affine Lie algebra aff(2,R). Furthermore, proved that the 2-form is symplectic and related to the 1-form. The result obtained is that the affine Lie algebra aff(2,R) has 1-form α=ε_12^*+ε_23^* on aff(2,R)^* which is related to its symplectic structure, β=ε_11^*∧ε_12^*+ε_12^*∧ε_22^*+ε_21^*∧ε_13^*+ε_22^*∧ε_23^* such that the affine Lie algebra aff(2,R) is a Frobenius Lie algebra. For further research, it can be developed into an affine Lie algebra with dimensions n(n+1).
Co-Authors Edi Kurniadi Firdaniza Firdaniza Kankan Parmikanti Pratiwi, Putri Nisa