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arXiv · 2404.12661

A Geometric Representation

Nicholas Phat Nguyen
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Abstract

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.

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Nicholas Phat Nguyen. 2024-04-19. A Geometric Representation. https://arxiv.org/abs/2404.12661

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