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1 results

  • Group-Theoretic Axioms For Projective Geometry

  • Alex D. Gottlieb, Joseph Lipman
  • Journal:
    Canadian Journal of Mathematics / Volume 43 / Issue 1 / 01 February 1991
    Published online by Cambridge University Press:
    20 November 2018, pp. 89-107
    Print publication:
    01 February 1991
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  • We show that a certain category 𝓖 whose objects are pairs G ⊃ H of groups subject to simple axioms is equivalent to the category of ≥ 2-dimensional vector spaces and injective semi-linear maps; and deduce via the "Fundamental Theorem of Projective Geometry" that the category of ≥ 2-dimensional projective spaces is equivalent to the quotient of a suitable subcategory of 𝓖 by the least equivalence relation which identifies conjugation by any element of H with the identity automorphism of G.