Reflections in Conics, Quadrics and Hyperquadrics via Clifford Algebra

2014/03/26 by Daniel Klawitter, Klawitter, Daniel
Mathematics · #15A66 #51B99 #51M15 #51N15 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #math.MG #msc:15A66 #msc:51B99 #msc:51M15 #msc:51N15

paper · pdf · doi:10.48550/arxiv.1403.6665

openalex publication_date 2014/03/26 · arxiv created 2014/09/16 · arxiv updated 2014/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal model is achieved. We discuss the geometric objects that can be represented. Furthermore, we show that the Pin group of this geometric algebra corresponds to inversions with respect to axis aligned quadrics. We discuss the construction for the two- and three-dimensional case in detail and give the construction for arbitrary dimension. Key Words: Clifford algebra, geometric algebra, generalized inversion, conic, quadric, hyperquadric

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