Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-03-12
Phys.Lett. B508 (2001) 173-183
Physics
High Energy Physics
High Energy Physics - Theory
12 pages, Revtex, v.2: typos corrected and references added
Scientific paper
10.1016/S0370-2693(01)00489-0
We consider the Gelfand-Dickey (GD) structure defined by the Moyal $\star$-product with parameter $\ka$, which not only defines the bi-Hamiltonian structure for the generalized Moyal KdV hierarchy but also provides a $W_n^{(\ka)}$ algebra containing the Virasoro algebra as a subalgebra with central charge $\ka^2(n^3-n)/3$. The free-field realization of the $W_n^{(\ka)}$ algebra is given through the Miura transformation and the cases for $W_3^{(\ka)}$ and $W_4^{(\ka)}$ are worked out in detail.
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