Projective metric geometry and Clifford algebras
Metric Geometry
2024-02-02 v2 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.2109.11470,
title = {Projective metric geometry and Clifford algebras},
author = {Hans Havlicek},
journal= {arXiv preprint arXiv:2109.11470},
year = {2024}
}
Comments
Owing to typographical errors by the author, the conditions on "dim V" appearing in the published version, formulas (2) and (3), fail to match with the cited sources. In the present text these mistakes have been remedied