Poisson Brackets and Structure of Nongraded Hamiltonian Lie Algebras Related to Locally-Finite Derivations

[摘要] Xu introduced a class of nongraded Hamiltonian Lie algebras. TheseLie algebras have a Poisson bracket structure. In this paper, theisomorphism classes of these Lie algebras are determined by employinga ``sandwich'' method and by studying some features of these Liealgebras. It is obtained that two Hamiltonian Lie algebras areisomorphic if and only if their corresponding Poisson algebras areisomorphic. Furthermore, the derivation algebras and the secondcohomology groups are determined.

[学科分类] 数学（综合）