Poisson algebras associated with constrained dispersionless modified Kadomtsev-Petviashvili hierarchies

We investigate the bi-Hamiltonian structures associated with constrained di spersionless modified Kadomtsev-Petviashvili (KP) hierarchies which are con structed from truncations of the Lax operator of the dmKP hierarchy. After transforming their second Hamiltonian structures to those of the Gelfand-Di ckey-type, we obtain the Poisson algebras of the coefficient functions of t he truncated Lax operators. Then we study the conformal property and free-f ield realizations of these Poisson algebras. Some examples are worked out e xplicitly to illustrate the obtained results. (C) 2000 American Institute o f Physics. [S0022-2488(00)02212-X].