BIHAMILTONIAN STRUCTURE OF THE KP HIERARCHY AND THE WKP ALGEBRA

We construct the second hamiltonian structure of the KP hierarchy as a natural extension of the Gel'fand-Dickey brackets of the generalized KdV hierarchies. The first structure - which has been recently identified as W 1 + infinity - is coordinated with the second structure and arises as a trivial (generalized) cocycle. The second structure gives rise to a non linear algebra, denoted W(KP), with generators of weights 1, 2, ... . The reduced algebra obtained by setting the weight 1 field to zero contains a centerless Virasoro subalgebra, and we argue that this is a universal W algebra from which all W(n) algebras are obtained through reduction.