  For a classical group $G$ over a field $F$ together with a finite-order
automorphism $\theta$ that acts compatibly on $F$, we describe the fixed point
subgroup of $\theta$ on $G$ and the eigenspaces of $\theta$ on the Lie algebra
$\mathfrak{g}$ in terms of cyclic quivers with involution. More precise
classification is given when $\mathfrak{g}$ is a loop Lie algebra, i.e., when
$F=\mathbb{C}((t))$.
