Relationships between fixed points and eigenvectors in the group "Equation missing" No EquationSource Format="TEX", only image and EquationSource Format="MATHML"

Abstract

Abstract P S L ( 2 , R ) is the most frequently studied subgroup of the Möbius transformations. By adding anti-automorphisms G ′ = { a ′ z + b ′ c ′ z + d ′ : a ′ , b ′ , c ′ , d ′ ∈ R , a ′ d ′ − b ′ c ′ = − 1 } to the group P S L ( 2 , R ) , the group G = P S L ( 2 , R ) ∪ G ′ is obtained. The elements of this group correspond to matrices of G L ( 2 , R ) . In this study, we consider the relationships between fixed points of the elements of the group G and eigenvectors of matrices corresponding to the elements of this group. MSC:20H10, 15A18.