The bracket of the exceptional Lie algebra E8
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913133096861696 |
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| author | Kollross, Andreas |
| author_facet | Kollross, Andreas |
| contents | We obtain an explicit formula for the bracket of the exceptional simple Lie algebra E8 based on triality and oct-octonions, following the Barton-Sudbery description of E8. Furthermore, we provide descriptions of the subalgebras E6 and E7 and prove an explicit formula for the 26-dimensional irreducible representation of F4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16513 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The bracket of the exceptional Lie algebra E8 Kollross, Andreas Differential Geometry Group Theory Rings and Algebras 17B25 (Primary) 17A35, 22E60, 53C35 (Secondary) We obtain an explicit formula for the bracket of the exceptional simple Lie algebra E8 based on triality and oct-octonions, following the Barton-Sudbery description of E8. Furthermore, we provide descriptions of the subalgebras E6 and E7 and prove an explicit formula for the 26-dimensional irreducible representation of F4. |
| title | The bracket of the exceptional Lie algebra E8 |
| topic | Differential Geometry Group Theory Rings and Algebras 17B25 (Primary) 17A35, 22E60, 53C35 (Secondary) |
| url | https://arxiv.org/abs/2504.16513 |