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Projective Cross-ratio on Hypercomplex Numbers

Abstract

The paper presents a new cross-ratio of hypercomplex numbers based on projective geometry. We discuss the essential properties of the projective cross-ratio, notably its invariance under Möbius transformations. Applications to the geometry of conic sections and Möbiusinvariant metrics on the upper half-plane are also given.

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Correspondence to Sky Brewer.

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Brewer, S. Projective Cross-ratio on Hypercomplex Numbers. Adv. Appl. Clifford Algebras 23, 1–14 (2013). https://doi.org/10.1007/s00006-012-0335-7

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  • DOI: https://doi.org/10.1007/s00006-012-0335-7

Keywords

  • Cross-ratio
  • Projective linear group
  • Möbius transformation
  • Cycles
  • SL(2,R)
  • Special linear group
  • Clifford algebra
  • dual numbers
  • double numbers