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

Killing boundary data for anti-de Sitter-like spacetimes