Lattice theory and metric geometry

• Autores: Horst Struve, Rolf Struve
• Localización: Algebra universalis, ISSN 0002-5240, Vol. 58, Nº. 4, 2008, págs. 461-477
• Idioma: inglés
• DOI: 10.1007/s00012-008-2081-1
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• Resumen

  • K. Menger and G. Birkhoff recognized 70 years ago that lattice theory provides a framework for the development of incidence geometry (affine and projective geometry). We show in this article that lattice theory also provides a framework for the development of metric geometry (including the euclidean and classical non-euclidean geometries which were first discovered by A. Cayley and F. Klein). To this end we introduce and study the concept of a Cayley�Klein lattice. A detailed investigation of the groups of automorphisms and an algebraic characterization of Cayley�Klein lattices are included.