INFINITE DIMENSIONAL LIE ALGEBRA WITH A NEW POISSON BRACKET 1)
新型Poisson括号意义下的无穷维Lie代数

For the Hamiltonian formulation of the Korteweg de Vires equation (KdVequation), C.S. Gardner defined a Poisson bracket. In this paper a brand new bracket is defined. It is easily verified that the new bracket possesses three properties of the Poisson bracket, bilinearity,skew symmetry, Jacobi identity. The new Poisson bracket has a close connection with C.S. Gardner's definition. In the framework of the new Poisson bracket, all the first integrals of the KdV equation constitute an infinite dimensional Lie algebra. Then the necessary and sufficient conditions for identifying the first integrals are obtained. Finally,the method for finding first integrals of KdV equation is investigated.