It has been known for some time that W algebras can be realised in terms of an energy-momentum tensor together with additional free scalar fields. Some recent results have shown that more general realisations are also possible. In this paper, we consider a wide class of realisations that may be obtained from the Miura transformation, related to the existence of canonical subalgebras of the Lie algebras on which the W algebras are based. We give explicit formulae for all realisations of this kind, and discuss their applications in W-string theory. 1992.
