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

Gökcan İ., Değer A. H.

Journal of New Theory, no.41, pp.35-50, 2022 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.53570/jnt.1161715
  • Journal Name: Journal of New Theory
  • Journal Indexes: TR DİZİN (ULAKBİM)
  • Page Numbers: pp.35-50
  • Karadeniz Technical University Affiliated: Yes


In this study, suborbital graphs, Gu,N" role="presentation" >Gu,N, and Fu,N" role="presentation" >Fu,N, are examined. Modular group Γ" role="presentation" >ΓΓ and its act on Q^" role="presentation" >ˆQ^ are studied. Lorentz matrix that gives the vertices obtained under the classical matrix multiplication in the suborbital graph Fu,N" role="presentation" >Fu,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 Γ" role="presentation" >ΓΓ is scrutinized. The vertices on the path starting with ∞" role="presentation" > are obtained under this element and the Lorentz matrix multiplication. For this path, it is shown that the vertices obtained in Fu,N" role="presentation" >Fu,N, under the Lorentz matrix multiplication with the Lorentz matrix satisfied the farthest vertex condition for the previous vertex.