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The KP hierarchy is hamiltonian relative to a one-parameter family of Poissonstructures obtained from a generalized Adler map in the space of formalpseudodifferential symbols with noninteger powers. The resulting $\W$-algebrais a one-parameter deformation of $\W_{\rm KP}$ admitting a central extensionfor generic values of the parameter, reducing naturally to $\W_n$ for specialvalues of the parameter, and contracting to the centrally extended$\W_{1+\infty}$, $\W_\infty$ and further truncations. In the classical limit,all algebras in the one-parameter family are equivalent and isomorphic to$\w_{\rm KP}$. The reduction induced by setting the spin-one field to zeroyields a one-parameter deformation of $\widehat{\W}_\infty$ which contracts toa new nonlinear algebra of the $\W_\infty$-type.Comment: 31 pages, compressed uuencoded .dvi file, BONN-HE-92/20, US-FT-7/92,  KUL-TF-92/20. [version just replaced was truncated by some mailer

A one-parameter family of hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear WKP algebra