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Global-Affine Morphisms of Projective Lattice Geometries

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Abstract

The fundamental theorem of projective geometry gives an algebraic representation of isomorphisms between projective geometries of dimension at least 3 over vector spaces and has been generalized in different ways. This note briefly presents some further generalizations which will be proved in the author’s thesis. We introduce the notion of global-affine morphisms between projective lattice geometries. Our investigations result in a general partial representation of global-affine morphisms which yields a complete representation of global-affine homomorphisms between large classes of module-induced projective geometries by semilinear mappings between the underlying modules.

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Duisburg, Lotharstraße 61, D-47057, Duisburg

    Marcus Greferath

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  1. Marcus Greferath
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This work was supported in part by a grant of the Zentrale Kommission für die Graduiertenförderung des Landes Rheinland-Pfalz. The author furthermore wishes to express his gratitude to S. E. Schmidt for a lot of comments and indispensible conceptual advice.

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Greferath, M. Global-Affine Morphisms of Projective Lattice Geometries. Results. Math. 24, 76–83 (1993). https://doi.org/10.1007/BF03322318

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