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Automorphisms of Hilbert's non-desarguesian affine plane and its projective closure
-
Thomas Schneider
and
Markus Stroppel
Published/Copyright:
November 22, 2007
Abstract
Hilbert constructed an early example of a non-desarguesian plane by modifying the lines of the real plane inside an ellipse. We employ methods from elementary algebraic geometry to show that the group of automorphisms of this plane leaves the ellipse invariant (unless the ellipse is a circle). Using this result, we determine the group of automorphisms of Hilbert's plane and some generalizations.
Key words: Hilbert; non-desarguesian; affine plane; projective plane; automorphism; collineation; inversion; algebraic curve; quadratic transformation
Received: 2006-05-12
Published Online: 2007-11-22
Published in Print: 2007-10-19
© Walter de Gruyter
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Articles in the same Issue
- Transitive projective planes
- Groups of type L2(q) acting on polytopes
- Automorphisms of Hilbert's non-desarguesian affine plane and its projective closure
- Isomorphisms of symplectic planes
- Paramétrisation des courbes multiples primitives
- Tight polyhedral models of isoparametric families, and PL-taut submanifolds
Keywords for this article
Hilbert;
non-desarguesian;
affine plane;
projective plane;
automorphism;
collineation;
inversion;
algebraic curve;
quadratic transformation
Articles in the same Issue
- Transitive projective planes
- Groups of type L2(q) acting on polytopes
- Automorphisms of Hilbert's non-desarguesian affine plane and its projective closure
- Isomorphisms of symplectic planes
- Paramétrisation des courbes multiples primitives
- Tight polyhedral models of isoparametric families, and PL-taut submanifolds
