Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912554128769024 |
|---|---|
| author | Hayashi, Takahiro |
| author_facet | Hayashi, Takahiro |
| contents | In this paper, we construct a partial group \(\mathcal{P}(F)\) that represents the "partial symmetry" inherent in a subset \(F\) of \(d\)-dimensional Euclidean space. In cases where \(F\) is not connected, \(\mathcal{P}(F)\) captures more detailed information than the conventional symmetry group \(G(F)\). To establish a stronger connection between \(\mathcal{P}(F)\) and \(F\), we introduce a novel definition of partial group action. Furthermore, to characterize \(\mathcal{P}(F)\) in specific cases, we define partial group actions on other partial groups and present a construction of the corresponding semidirect product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_14304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins Hayashi, Takahiro Group Theory Quantum Algebra 18N50, 51M20, 08A99 In this paper, we construct a partial group \(\mathcal{P}(F)\) that represents the "partial symmetry" inherent in a subset \(F\) of \(d\)-dimensional Euclidean space. In cases where \(F\) is not connected, \(\mathcal{P}(F)\) captures more detailed information than the conventional symmetry group \(G(F)\). To establish a stronger connection between \(\mathcal{P}(F)\) and \(F\), we introduce a novel definition of partial group action. Furthermore, to characterize \(\mathcal{P}(F)\) in specific cases, we define partial group actions on other partial groups and present a construction of the corresponding semidirect product. |
| title | Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins |
| topic | Group Theory Quantum Algebra 18N50, 51M20, 08A99 |
| url | https://arxiv.org/abs/2506.14304 |