Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations

Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations

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摘要 We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras （or corresponding Hamiltonian operators） associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu＇s generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility. We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras （or corresponding Hamiltonian operators） associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu＇s generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.

作者 Ling CHEN

机构地区 Institute of Applied Mathematics

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第1期45-72,共28页 数学学报（英文版）

基金 Supported by National Natural Science Foundation of China （Grant No. 10871193）

关键词 Hamiltonian Lie algebras representation SIMPLICITY IRREDUCIBILITY Hamiltonian Lie algebras, representation, simplicity, irreducibility

分类号 O152.5 [理学—基础数学] O413.1 [理学—理论物理]

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Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations

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