Journal of Lie Theory

no. 1
Composition Series for a Family of Modules of Nongraded Hamiltonial Type Lie Algebras
Yufeng Zhao1
1LAMA, School of Mathematical Sciences, Peking University, Beijing, 100871, China
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

Yufeng Zhao  1

1 LAMA, School of Mathematical Sciences, Peking University, Beijing, 100871, China 
Yufeng 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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