Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra

Advances in Applied Clifford Algebras volume 31, Article number: 18 (2021) Cite this article

Abstract

We show that if Projective Geometric Algebra (PGA), i.e. the geometric algebra with degenerate signature (n, 0, 1), is understood as a subalgebra of Conformal Geometric Algebra (CGA) in a mathematically correct sense, then flat primitives share the same representation in PGA and CGA. Particularly, we treat duality in PGA in the framework of CGA. This leads to unification of PGA and CGA primitives which is important especially for software implementation and symbolic calculations.

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Affiliations

  1. Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic

    Jaroslav Hrdina, Aleš Návrat & Petr Vašík

  2. Informatics Institute, Faculty of Science, University of Amsterdam, Amsterdam, The Netherlands

    Leo Dorst

Authors
  1. Jaroslav Hrdina
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  2. Aleš Návrat
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  3. Petr Vašík
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  4. Leo Dorst
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Corresponding author

Correspondence to Aleš Návrat.

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The first three authors were supported by a Grant No.: FSI-S-20-6187.

Communicated by Dietmar Hildenbrand.

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Hrdina, J., Návrat, A., Vašík, P. et al. Projective Geometric Algebra as a Subalgebra of Conformal Geometric algebra. Adv. Appl. Clifford Algebras 31, 18 (2021). https://doi.org/10.1007/s00006-021-01118-7

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Keywords

  • Conformal geometric algebra
  • Projective geometric algebra
  • Euclidean geometry

Mathematics Subject Classification

  • Primary 15A66
  • Secondary 51N25