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

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Atıf İçin Kopyala

Gökcan İ., Değer A. H.

Journal of New Theory, sa.41, ss.35-50, 2022 (Hakemli Dergi)

• Yayın Türü: Makale / Tam Makale
• Basım Tarihi: 2022
• Doi Numarası: 10.53570/jnt.1161715
• Dergi Adı: Journal of New Theory
• Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.35-50
• Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

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" >Γ$\mathrm{\Gamma }$ and its act on Q^" role="presentation" >ˆQ$\widehat{\mathbb{�}}$ 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" >Γ$\mathrm{\Gamma }$ is scrutinized. The vertices on the path starting with ∞" role="presentation" >∞$\mathrm{\infty }$ 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.