  Given an initial-boundary value problem for an anti-de Sitter-like spacetime,
we analyse conditions on the conformal boundary ensuring the existence of
Killing vectors in the spacetime arising from this problem. This analysis makes
use of a system of conformal wave equations describing the propagation of the
Killing equation first considered by Paetz. We identify an obstruction tensor
constructed from Killing vector candidate and the Cotton tensor of the
conformal boundary whose vanishing is a necessary condition for the existence
of Killing vectors in the spacetime. This obstruction tensor vanishes if the
conformal boundary is conformally flat.
