Poisson brackets and structure of nongraded Hamiltonian Lie algebras related to locally-finite derivations

Details Poisson brackets and structure of nongraded Hamiltonian Lie algebras related to locally-finite derivations Poisson brackets and structure of nongraded Hamiltonian Lie algebras related to locally-finite derivations

2003-04-05

arxiv.org/abs/math/0304073v1

Mathematics

Quantum Algebra

36 pages, latex; to appear in Canadian J. Math

Scientific paper

A class of nongraded Hamiltonian Lie algebras was earlier introduced by Xu. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a ``sandwich'' method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson algebras are isomorphic. Furthermore, the derivation algebras and the second cohomology groups are determined.

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