Extended Conformal Algebras Associated with Constrained KP Hierarchy

We examine the conformal preperty of the second Hamiltonian structure of constrained KP hierarchy derived by Oevel and Strampp. We find that it naturally gives a family of nonlocal extended conformal algebras. We give two examples of such algebras and find that they are similar to Bilal's V algebra. By taking a gauge transformation one can map the constrained KP hierarchy to Kupershmidt's nonstardard Lax hierarchy. We consider the second Hamiltonian structure in this representation. We show that after mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We show that this Hamiltonian structure defines the W-U(1)-Kac-Moody algebra by working out its conformally covariant form.