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arXiv · 2109.11470

Projective metric geometry and Clifford algebras

Hans Havlicek
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Abstract

Each vector space that is endowed with a quadratic form determines its Clifford algebra. This algebra, in turn, contains a distinguished group, known as the Lipschitz group. We show that only a quotient of this group remains meaningful in the context of projective metric geometry. This quotient of the Lipschitz group can be viewed as a point set in the projective space on the Clifford algebra and, under certain restrictions, leads to an algebraic description of so-called kinematic mappings.

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Hans Havlicek. 2021-09-23. Projective metric geometry and Clifford algebras. https://doi.org/10.1007/s00025-021-01516-0

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