is the very first observation leading to the AdS/CFT correspondence conjectures in physics. See also Bilinear transform Conformal geometry Fuchsian group Generalised circle Hyperbolic geometry Infinite compositions of analytic functions Inversion transformation Kleinian group Lie sphere geometry Linear fractional transformation Liouville's theorem (conformal mappings) Lorentz group Modular group Poincaré half-plane model Projective geometry Projective line over a ring Representation theory of the Lorentz group Schottky group Notes References Specific General (See Chapter 6 for the classification, up to conjugacy, of the Lie subalgebras of the Lie algebra of the Lorentz group.) See Chapter 2. . (See Chapters 3–5 of this classic book for a beautiful introduction to the Riemann sphere, stereographic projection, and Möbius transformations.) (Aimed at non-mathematicians, provides an excellent exposition of theory and results, richly illustrated with diagrams.) (See Chapter 3 for a beautifully illustrated introduction to Möbius transformations, including their classification up to conjugacy.) (See Chapter 2 for an introduction to Möbius transformations.) Further reading External links Conformal maps gallery Projective geometry Conformal geometry Lie groups Riemann surfaces Functions and mappings Kleinian groups Conformal mappings