  Automorphisms of order $2$ are studied in order to understand generalized
symmetric spaces. The groups of type $E_6$ we consider here can be realized as
both the group of linear maps that leave a certain determinant invariant, and
also as the identity component of the automorphism group of a class of
structurable algebras known as Brown algebras. We will classify the
$k$-involutions of these groups of type $E_6$ using aspects of both
descriptions, and give detailed descriptions of representatives over certain
fields including algebraically closed fields, $\mathbb{R}$, $\mathbb{F}_p$, and
$\mathbb{Q}_p$.
