The subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909764922900480 |
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| author | Douglas, Andrew de Graaf, Willem A. |
| author_facet | Douglas, Andrew de Graaf, Willem A. |
| contents | We classify the real subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$, a non-compact real form of the complex special linear algebra $\mathfrak{sl}_3(\mathbb{C})$. Our approach combines Galois cohomology with the existing classification of complex subalgebras of $\mathfrak{sl}_3(\mathbb{C})$. This work completes the classification of real subalgebras of the non-compact real forms of $\mathfrak{sl}_3(\mathbb{C})$, since those of $\mathfrak{sl}_3(\mathbb{R})$ have already been classified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$ Douglas, Andrew de Graaf, Willem A. Group Theory 17B05, 17B20, 17B30, 20G10, 20G20 We classify the real subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$, a non-compact real form of the complex special linear algebra $\mathfrak{sl}_3(\mathbb{C})$. Our approach combines Galois cohomology with the existing classification of complex subalgebras of $\mathfrak{sl}_3(\mathbb{C})$. This work completes the classification of real subalgebras of the non-compact real forms of $\mathfrak{sl}_3(\mathbb{C})$, since those of $\mathfrak{sl}_3(\mathbb{R})$ have already been classified. |
| title | The subalgebras of the generalized special unitary algebra $\mathfrak{su}(2,1)$ |
| topic | Group Theory 17B05, 17B20, 17B30, 20G10, 20G20 |
| url | https://arxiv.org/abs/2504.17942 |