Journal of Lie Theory

no. 1
Composition Series for a Family of Modules of Nongraded Hamiltonial Type Lie Algebras
Journal of Lie Theory, Volume 19 (2009) no. 1, pp. 1-27
Nongraded infinite-dimensional simple Lie algebras of Hamiltonial type were constructed by Xu related to pairs of locally-finite derivations on certain commutative associative algebras. In this paper, we construct a family of modules with parameters for nongraded Hamiltonial type Lie algebras based on finite-dimensional irreducible modules of symplectic Lie algebras. When the corresponding modules of symplectic Lie algebras are finite-dimensional irreducible weight modules whose weight spaces are all one-dimensional, we get a composition series for these modules and an explicit construction of the composition series are also given by means of the exterior algebra powers.
DOI: 10.5802/jolt.539
Classification: 17B10, 17B65
Keywords: Nongraded Hamiltonial type Lie algebras, representations of nongraded Hamiltonial type Lie algebras 
@article{JOLT_2009_19_1_a0,
     author = {Y. Zhao},
     title = {Composition {Series} for a {Family} of {Modules} of {Nongraded} {Hamiltonial} {Type} {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {1--27},
     year = {2009},
     volume = {19},
     number = {1},
     doi = {10.5802/jolt.539},
     zbl = {1186.17005},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.539/}
}
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Y. Zhao. Composition Series for a Family of Modules of Nongraded Hamiltonial Type Lie Algebras. Journal of Lie Theory, Volume 19 (2009) no. 1, pp. 1-27. doi: 10.5802/jolt.539

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