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We investigate the bi-Hamiltonian structures associated with constraineddispersionless modified KP hierarchies which are constructed from truncationsof the Lax operator of the dispersionless modified KP hierarchy. Aftertransforming their second Hamiltonian structures to those of Gelfand-Dickeytype, we obtain the Poisson algebras of the coefficient functions of thetruncated Lax operators. Then we study the conformal property and free-fieldrealizations of these Poisson algebras. Some examples are worked out explicitlyto illustrate the obtained results.Comment: 15 pages, latex, no figure

Poisson algebras associated with constrained dispersionless modified Kadomtsev–Petviashvili hierarchies