Science Fair Project Encyclopedia
Klein quartic
The Klein quartic x3y + y3z + z3x = 0, named after Felix Klein, is a Riemann surface, and a curve of genus 3 over the complex numbers C.
The Klein quartic has automorphism group isomorphic to the projective special linear group G = PSL(2,7). The order 168 of G is the maximum allowed for this genus 3; and this curve is uniquely determined by requiring that the symmetry is as large as this.
Klein's quartic occurs all over mathematics, in contexts including representation theory, homology theory, octonion multiplication, Fermat's Last Theorem, and Stark's theorem on imaginary quadratic number fields of class number 1.
External links
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details