Standard automorphisms of semisimple Lie algebras and their relations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918128599957504 |
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| author | Reynoso-Mercado, David |
| author_facet | Reynoso-Mercado, David |
| contents | Let $\mathfrak{g}$ be the simple Lie algebra of square matrices $(n+1)\times (n+1)$ with zero trace. There are certain relations concerning standard automorphisms that are considered ``folklore". One can find a complete proof of these in Millson and Toledano Laredo's work [Transformation Groups, Vol. 10, No. 2, 2005, pp. 217-254], but said proof is based on topological arguments which are non-trivial. The aim of this work is to verify these relations in an elementary way. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_15256 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Standard automorphisms of semisimple Lie algebras and their relations Reynoso-Mercado, David Rings and Algebras 17B10, 20F36 Let $\mathfrak{g}$ be the simple Lie algebra of square matrices $(n+1)\times (n+1)$ with zero trace. There are certain relations concerning standard automorphisms that are considered ``folklore". One can find a complete proof of these in Millson and Toledano Laredo's work [Transformation Groups, Vol. 10, No. 2, 2005, pp. 217-254], but said proof is based on topological arguments which are non-trivial. The aim of this work is to verify these relations in an elementary way. |
| title | Standard automorphisms of semisimple Lie algebras and their relations |
| topic | Rings and Algebras 17B10, 20F36 |
| url | https://arxiv.org/abs/2401.15256 |