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

Published online by Cambridge University Press:  20 November 2018

Yucai Su*
Affiliation:
Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, P. R. China email: [email protected]
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Abstract

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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.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2003

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