Conjugate reversibility in complex special linear groups

Krishnendu Gongopadhyay; Rahul Mondal

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arXiv · 2506.15336

Conjugate reversibility in complex special linear groups

Krishnendu Gongopadhyay·Rahul Mondal

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Abstract

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.

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BibTeX RIS

Krishnendu Gongopadhyay, Rahul Mondal. 2025-06-18. Conjugate reversibility in complex special linear groups. https://arxiv.org/abs/2506.15336

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