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$W_n^{(\ka)}$ algebra associated with the Moyal KdV Hierarchy

Ming-Hsien Tu
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Abstract

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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Ming-Hsien Tu. 2001-04-30. $W_n^{(\ka)}$ algebra associated with the Moyal KdV Hierarchy. https://doi.org/10.1016/s0370-2693(01)00489-0

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