Centrally extended W1+∞ and the KP hierarchy

It is well known that the centerless W1+∞ algebra provides a hamiltonian structure for the KP hierarchy. In this letter we address the question whether the centerful version plays a similar rôle in any related integrable system. We find that, surprisingly enough, the centrally extended W1+∞ algebra yields yet another Poisson structure for the same standard KP hierarchy. This is proven by explicit construction of the infinitely many new hamiltonians in closed form.