Advances in Applied Clifford Algebras

, Volume 23, Issue 1, pp 1–14

Projective Cross-ratio on Hypercomplex Numbers


DOI: 10.1007/s00006-012-0335-7

Cite this article as:
Brewer, S. Adv. Appl. Clifford Algebras (2013) 23: 1. doi:10.1007/s00006-012-0335-7


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.


Cross-ratioProjective linear groupMöbius transformationCyclesSL(2,R)Special linear groupClifford algebradual numbersdouble numbers

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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.School of MathematicsLeeds UniversityLeedsEngland