Projective metric geometry and Clifford algebras
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2021
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914661628116992 |
|---|---|
| author | Havlicek, Hans |
| author_facet | Havlicek, Hans |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_11470 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Projective metric geometry and Clifford algebras Havlicek, Hans Metric Geometry Rings and Algebras 51F25 15A66 51F15 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. |
| title | Projective metric geometry and Clifford algebras |
| topic | Metric Geometry Rings and Algebras 51F25 15A66 51F15 |
| url | https://arxiv.org/abs/2109.11470 |