Advances in Applied Clifford Algebras

, Volume 23, Issue 1, pp 1-14

First online:

Projective Cross-ratio on Hypercomplex Numbers

  • Sky BrewerAffiliated withSchool of Mathematics, Leeds University Email author 

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