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 W n ( κ) algebra containing the Virasoro algebra as a subalgebra with central charge κ 2( n 3− n)/3. The free-field realization of the W n ( κ) algebra is given through the Miura transformation and the cases for W 3 ( κ) and W 4 ( κ) are worked out in detail.
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