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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
Yucai Su*
Affiliation:
Department of Mathematics, Shanghai Jiaotong University, Shanghai 200030, P. R. China email: ycsu@sjtu.edu.cn
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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

17B4017B65
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 4 , 01 August 2003 , pp. 856 - 896
Copyright
Copyright © Canadian Mathematical Society 2003

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