A note on adjoint reality in simple complex Lie algebras
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913342722932736 |
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| author | Gongopadhyay, Krishnendu Maity, Chandan |
| author_facet | Gongopadhyay, Krishnendu Maity, Chandan |
| contents | Let $G$ be a Lie group with Lie algebra $\mathfrak g$. In the paper "Reality of unipotent elements in simple Lie groups, Bull. Sci. Math., 185, 2023, 103261" by K. Gongopadhyay and C. Maity, an infinitesimal version of the notion of classical reality, namely adjoint reality, has been introduced. An element $X \in \mathfrak g$ is adjoint real if $-X$ belongs to the adjoint orbit of $X$ in $\mathfrak g$. In this paper, we investigate the adjoint real and the strongly adjoint real semisimple elements in complex simple classical Lie algebras. We also prove that every element in a complex symplectic Lie algebra is adjoint real. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on adjoint reality in simple complex Lie algebras Gongopadhyay, Krishnendu Maity, Chandan Group Theory Primary 20E45, Secondary 22E60, 17B08 Let $G$ be a Lie group with Lie algebra $\mathfrak g$. In the paper "Reality of unipotent elements in simple Lie groups, Bull. Sci. Math., 185, 2023, 103261" by K. Gongopadhyay and C. Maity, an infinitesimal version of the notion of classical reality, namely adjoint reality, has been introduced. An element $X \in \mathfrak g$ is adjoint real if $-X$ belongs to the adjoint orbit of $X$ in $\mathfrak g$. In this paper, we investigate the adjoint real and the strongly adjoint real semisimple elements in complex simple classical Lie algebras. We also prove that every element in a complex symplectic Lie algebra is adjoint real. |
| title | A note on adjoint reality in simple complex Lie algebras |
| topic | Group Theory Primary 20E45, Secondary 22E60, 17B08 |
| url | https://arxiv.org/abs/2405.03392 |