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Twisted Hamiltonian Lie algebras and their multiplicity-free representations

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Abstract

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.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Ling Chen

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  1. Ling Chen
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Correspondence to Ling Chen.

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

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Chen, L. Twisted Hamiltonian Lie algebras and their multiplicity-free representations. Acta. Math. Sin.-English Ser. 27, 45–72 (2011). https://doi.org/10.1007/s10114-011-0204-7

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  • DOI: https://doi.org/10.1007/s10114-011-0204-7

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