$W_n^{(\ka)}$ algebra associated with the Moyal KdV Hierarchy
arXiv:hep-th/0103083 · doi:10.1016/S0370-2693(01)00489-0
Abstract
We consider the Gelfand-Dickey (GD) structure defined by the Moyal -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.
12 pages, Revtex, v.2: typos corrected and references added