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

Open Access article
 Printed: Aug 2003
  • Yucai Su
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Xu introduced a class of nongraded Hamiltonian Lie algebras. 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.
MSC Classifications: 17B40, 17B65 show english descriptions Automorphisms, derivations, other operators
Infinite-dimensional Lie (super)algebras [See also 22E65]
17B40 - Automorphisms, derivations, other operators
17B65 - Infinite-dimensional Lie (super)algebras [See also 22E65]

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