Twisted Hamiltonian Lie Algebras and Their Multiplicity-Free Representations  

作　　者：Ling CHEN 

机构地区：[1]Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》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）

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.

关 键 词：Hamiltonian Lie algebras representation SIMPLICITY IRREDUCIBILITY 

分 类 号：O152.5[理学—数学] O413.1[理学—基础数学]