Conjugate reversibility in complex special linear groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916799298142208 |
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| author | Gongopadhyay, Krishnendu Mondal, Rahul |
| author_facet | Gongopadhyay, Krishnendu Mondal, Rahul |
| contents | We introduce and study conjugate reversibility (or $c$-reversibility) in the complex special linear group $\SL(n,\C)$ where an element is conjugate to the inverse of its complex conjugate. We prove that in $\SL(n, \C)$, every $c$-reversible element is strongly $c$-reversible. We provide a complete classification of $c$-reversible elements based on their conjugacy invariants. This leads to an algebraic characterization of projective transformations. As a special case, a finer classification in $\SL(4, \C)$ is obtained in terms of trace conditions and resultant computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjugate reversibility in complex special linear groups Gongopadhyay, Krishnendu Mondal, Rahul Group Theory We introduce and study conjugate reversibility (or $c$-reversibility) in the complex special linear group $\SL(n,\C)$ where an element is conjugate to the inverse of its complex conjugate. We prove that in $\SL(n, \C)$, every $c$-reversible element is strongly $c$-reversible. We provide a complete classification of $c$-reversible elements based on their conjugacy invariants. This leads to an algebraic characterization of projective transformations. As a special case, a finer classification in $\SL(4, \C)$ is obtained in terms of trace conditions and resultant computations. |
| title | Conjugate reversibility in complex special linear groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2506.15336 |