Strongly reversible classes in $\mathrm{SL}(n,\mathbb{C})$

TL;DR

This paper characterizes and classifies strongly reversible elements in the special linear group over complex numbers, providing necessary and sufficient conditions for elements to be expressed as products of two involutions.

Contribution

It offers a complete classification of strongly reversible conjugacy classes in SL(n,C), including necessary and sufficient conditions for elements to be products of two involutions.

Findings

Necessary and sufficient conditions for strong reversibility in SL(n,C)

Complete classification of strongly reversible conjugacy classes

Identification of properties distinguishing strongly reversible elements

Abstract

An element of a group is called $\textit{strongly reversible}$ or $\textit{strongly real}$ if it can be expressed as a product of two involutions. We provide necessary and sufficient conditions for an element of $\mathrm{SL}(n,\mathbb{C})$ to be a product of two involutions. In particular, we classify the strongly reversible conjugacy classes in $\mathrm{SL}(n,\mathbb{C})$.