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Möbius Group

The equation

x_1^2+x_2^2+...+x_n^2-2x_0x_infty=0

represents an n-dimensional hypersphere S^n as a quadratic hypersurface in an (n+1)-dimensional real projective space P^(n+1), where x_a are homogeneous coordinates in P^(n+1). Then the group M(n) of projective transformations which leave S^n invariant is called the Möbius group.

See also

Modular Group Gamma

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References

Itô, K. (Ed.). "Möbius Geometry." §76A in Encyclopedic Dictionary of Mathematics, 2nd ed., Vol. 1. Cambridge, MA: MIT Press, pp. 287-288, 1986.Iyanaga, S. and Kawada, Y. (Eds.). "Möbius Geometry." §78A in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 265-266, 1980.

Referenced on Wolfram|Alpha

Möbius Group

Cite this as:

Weisstein, Eric W. "Möbius Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MoebiusGroup.html

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