  Let $ G $ be a Lie group with Lie algebra $ \mathfrak{g} $. An element $ X
\in \mathfrak{g} $ is called $\mathrm{Ad}_G$-real if $ -X=gXg^{-1} $ for some $
g \in G $. Moreover, if $ -X=gXg^{-1} $ holds for some involution $ g\in G $,
then $ X $ is called strongly $\mathrm{Ad}_G$-real. We have classified the
$\mathrm{Ad}_G$-real and the strongly $\mathrm{Ad}_G$-real orbits in the
special linear Lie algebra $\mathfrak{sl}(n,\mathbb{F}) $ for $
\mathbb{F}=\mathbb{C}$ or $\mathbb{H} $.
