  Let $\gg$ be a simple, finite-dimensional complex Lie algebra, and let
$V^k(\gg)$ denote the universal affine vertex algebra associated to $\gg$ at
level $k$. The Cartan involution on $\gg$ lifts to an involution on $V^k(\gg)$,
and we denote by $V^k(\gg)^{\mathbb{Z}_2}$ the orbifold, or fixed-point
subalgebra, under this involution. Our main result is an explicit minimal
strong finite generating set for $V^k(\gg)^{\mathbb{Z}_2}$ for generic values
of $k$. In the case $\gg = \gs\gl_2$, we also determine the set of nongeneric
values of $k$, where this set does not work.
