Abstract :
We consider the Gelfand–Dickey (GD) structure defined by the Moyal ★-product with parameter κ, which not only defines the bi-Hamiltonian structure for the generalized Moyal KdV hierarchy but also provides a Wn(κ) algebra containing the Virasoro algebra as a subalgebra with central charge κ2(n3−n)/3. The free-field realization of the Wn(κ) algebra is given through the Miura transformation and the cases for W3(κ) and W4(κ) are worked out in detail.
