Geometry of gyrogroups via Klein's approach
| Autor: | Suksumran, Teerapong |
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| Rok vydání: | 2021 |
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| Zdroj: | Mediterranean Journal of Mathematics 19, no. 4 (2022), Article 148 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00009-022-02051-0 |
| Popis: | Using Klein's approach, geometry can be studied in terms of a space of points and a group of transformations of that space. This allows us to apply algebraic tools in studying geometry of mathematical structures. In this article, we follow Klein's approach to study the geometry $(G, \mathcal{T})$, where $G$ is an abstract gyrogroup and $\mathcal{T}$ is an appropriate group of transformations containing all gyroautomorphisms of $G$. We focus on $n$-transitivity of gyrogroups and also give a few characterizations of coset spaces to be minimally invariant sets. We then prove that the collection of open balls of equal radius is a minimally invariant set of the geometry $(G, \Gamma_m)$ for any normed gyrogroup $G$, where $\Gamma_m$ is a suitable group of isometries of $G$. Comment: 20 pages |
| Databáze: | arXiv |
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