Conformal Covariance Subalgebras

We give a direct Lie algebraic characterisation of conformal inclusions of chiral current algebras associated with compact, reductive Lie algebras. We use straightforward quantum field theoretic arguments and prove a long standing conjecture of Schellekens and Warner on grounds of unitarity and positivity of energy. We explore the structures found to characterise ``conformal covariance subalgebras'' and ``coset current algebras''.