科研之友
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摘要
Let be the polynomial algebra on two variables x, y over an algebraically closed field of characteristic zero. Under the Poisson bracket, is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of induced from the multiplication of the associative commutative algebra coincides with the maximal good subspace of induced from the Poisson bracket of the Poisson Lie algebra . Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products, five classes of new infinite-dimensional Lie algebras are obtained.
