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Reflections in conics, quadrics and hyperquadrics via Clifford algebra

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Abstract

In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal geometric algebra 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 the group of inversions with respect to quadrics in principal position. We discuss the construction for the two- and three-dimensional case in detail and give the construction for arbitrary dimension.

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Acknowledgments

This work was supported by the research project “Line Geometry for Lightweight Structures”, funded by the DFG (German Research Foundation) as part of the SPP 1542.

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Authors and Affiliations

  1. Institute of Geometry, Technical University of Dresden, Zellescher Weg 12-14, 01062, Dresden, Germany

    Daniel Klawitter

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  1. Daniel Klawitter
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Correspondence to Daniel Klawitter.

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Klawitter, D. Reflections in conics, quadrics and hyperquadrics via Clifford algebra. Beitr Algebra Geom 57, 221–242 (2016). https://doi.org/10.1007/s13366-014-0218-2

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  • DOI: https://doi.org/10.1007/s13366-014-0218-2

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