A ONE-PARAMETER FAMILY OF HAMILTONIAN STRUCTURES FOR THE KP HIERARCHY AND A CONTINUOUS DEFORMATION OF THE NONLINEAR W(KP) ALGEBRA

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting W-algebra is a one-parameter deformation of W(KP) admitting a central extension for generic values of the parameter, reducing naturally to W(n) for special values of the parameter, and contracting to the centrally extended W1+infinity, W(infinity) and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic to W(KP). The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of W(infinity) which contracts to a new nonlinear algebra of the W(infinity)-type.