SYMPLECTIC STRUCTURES FROM CENTRAL EXTENSION OF W-1+INFINITY ALGEBRA AND KP EQUATION

We modify the first symplectic structure of KP hierarchy by considerin g its relation with W-1+infinity algebra and introducing its central e xtension ($) over tilde W-1+infinity. We show that at least the first five Hamiltonians of modified KP hierarchy can be chosen to be conserv ed, in involution with respect to the symplectic bracket generated by ($) over tilde W-1+infinity. It appears that from the first four flows of modified KP hierarchy we shall obtain the same (2 + 1)dimensional standard KP equation. We provide therefore the one-parameter family of Hamiltonians and symplectic structures describing the standard KP equ ation.