  Let $G$ be a Lie group with Lie algebra $\mathfrak g$. In the paper "Reality
of unipotent elements in simple Lie groups, Bull. Sci. Math., 185, 2023,
103261" by K. Gongopadhyay and C. Maity, an infinitesimal version of the notion
of classical reality, namely adjoint reality, has been introduced. An element
$X \in \mathfrak g$ is adjoint real if $-X$ belongs to the adjoint orbit of $X$
in $\mathfrak g$. In this paper, we investigate the adjoint real and the
strongly adjoint real semisimple elements in complex simple classical Lie
algebras. We also prove that every element in a complex symplectic Lie algebra
is adjoint real.
