Real adjoint orbits of special linear groups
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929325761101824 |
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| author | Gongopadhyay, Krishnendu Lohan, Tejbir Maity, Chandan |
| author_facet | Gongopadhyay, Krishnendu Lohan, Tejbir Maity, Chandan |
| contents | Let $ G $ be a Lie group with Lie algebra $ \mathfrak{g} $. An element $ X \in \mathfrak{g} $ is called $\mathrm{Ad}_G$-real if $ -X=gXg^{-1} $ for some $ g \in G $. Moreover, if $ -X=gXg^{-1} $ holds for some involution $ g\in G $, then $ X $ is called strongly $\mathrm{Ad}_G$-real. We have classified the $\mathrm{Ad}_G$-real and the strongly $\mathrm{Ad}_G$-real orbits in the special linear Lie algebra $\mathfrak{sl}(n,\mathbb{F}) $ for $ \mathbb{F}=\mathbb{C}$ or $\mathbb{H} $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_03624 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Real adjoint orbits of special linear groups Gongopadhyay, Krishnendu Lohan, Tejbir Maity, Chandan Group Theory 20E45 (Primary) 22E60, 20G20 (Secondary) [2020] Let $ G $ be a Lie group with Lie algebra $ \mathfrak{g} $. An element $ X \in \mathfrak{g} $ is called $\mathrm{Ad}_G$-real if $ -X=gXg^{-1} $ for some $ g \in G $. Moreover, if $ -X=gXg^{-1} $ holds for some involution $ g\in G $, then $ X $ is called strongly $\mathrm{Ad}_G$-real. We have classified the $\mathrm{Ad}_G$-real and the strongly $\mathrm{Ad}_G$-real orbits in the special linear Lie algebra $\mathfrak{sl}(n,\mathbb{F}) $ for $ \mathbb{F}=\mathbb{C}$ or $\mathbb{H} $. |
| title | Real adjoint orbits of special linear groups |
| topic | Group Theory 20E45 (Primary) 22E60, 20G20 (Secondary) [2020] |
| url | https://arxiv.org/abs/2204.03624 |