Vertices of Suborbital Graph $F_{u,N}$ under Lorentz Matrix Multiplication

Authors : Ibrahim Gökcan, Ali Hikmet Değer

Pages : 35-50

Doi:10.53570/jnt.1161715

View : 16 | Download : 9

Publication Date : 2022-12-31

Article Type : Research

Abstract :In this study, suborbital graphs, $G_{u,N}$ and $F_{u,N}$ are examined. Modular group $\\Gamma$ and its act on $\\widehat{\\mathbb{Q}}$ are studied. Lorentz matrix that gives the vertices obtained under the classical matrix multiplication in the suborbital graph $F_{u,N}$ is analysed with the Lorentz matrix multiplication. Lorentz matrix written as Möbius transform is normalized and the type of the transform is researched. Moreover, a different element of Modular group $\\Gamma$ is scrutinized. The vertices on the path starting with $\\infty$ are obtained under this element and the Lorentz matrix multiplication. For this path, it is shown that the vertices obtained in $F_{u,N}$ under the Lorentz matrix multiplication with the Lorentz matrix satisfied the farthest vertex condition for the previous vertex.
Keywords : Lorentz matrix multiplication, Modular group, Möbius Transform