Regular Solids and Isolated Singularities pp 32-68 | Cite as
Finite Subgroups of SL(2, C) and Invariant Polynomials
Chapter
Abstract
In the first chapter the finite subgroups Γ of S0(3) have been classified using their action on the Euclidean two-sphere S2. Now S2 is considered as Riemannian sphere, i.e. as Gauss plane ℂ of the complex variable z compactified by one point ∞. Then S0(3) and hence every finite subgroup Γ acts by projective (linear, homographic) transformations
$${\rm z} \mapsto {{{\rm az + b}} \over {{\rm cz + d}}}\,\,\,{\rm with}\,\,\,{\rm ad - bc} \ne {\rm 0}{\rm.}$$
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© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig 1986