English

Conjugate reversibility in complex special linear groups

Group Theory 2025-06-19 v1

Abstract

We introduce and study conjugate reversibility (or cc-reversibility) in the complex special linear group \SL(n,\C)\SL(n,\C) where an element is conjugate to the inverse of its complex conjugate. We prove that in \SL(n,\C)\SL(n, \C), every cc-reversible element is strongly cc-reversible. We provide a complete classification of cc-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)\SL(4, \C) is obtained in terms of trace conditions and resultant computations.

Keywords

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}
}
R2 v1 2026-07-01T03:23:24.795Z