Conjugate reversibility in complex special linear groups
Group Theory
2025-06-19 v1
Abstract
We introduce and study conjugate reversibility (or -reversibility) in the complex special linear group where an element is conjugate to the inverse of its complex conjugate. We prove that in , every -reversible element is strongly -reversible. We provide a complete classification of -reversible elements based on their conjugacy invariants. This leads to an algebraic characterization of projective transformations. As a special case, a finer classification in is obtained in terms of trace conditions and resultant computations.
Cite
@article{arxiv.2506.15336,
title = {Conjugate reversibility in complex special linear groups},
author = {Krishnendu Gongopadhyay and Rahul Mondal},
journal= {arXiv preprint arXiv:2506.15336},
year = {2025}
}