A Geometric Representation
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911845826166784 |
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| author | Nguyen, Nicholas Phat |
| author_facet | Nguyen, Nicholas Phat |
| contents | This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This geometric representation depends on the theory of inversive transformations in dimension 1 as outlined in the 2021 article Projective Line Revisited by the same author. This geometric representation also provides a new perspective on some classical properties of the projective line, such as the classical cross ratio. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Geometric Representation Nguyen, Nicholas Phat History and Overview This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of projective transformations of a projective line. This geometric representation depends on the theory of inversive transformations in dimension 1 as outlined in the 2021 article Projective Line Revisited by the same author. This geometric representation also provides a new perspective on some classical properties of the projective line, such as the classical cross ratio. |
| title | A Geometric Representation |
| topic | History and Overview |
| url | https://arxiv.org/abs/2404.12661 |