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Journal of Lie Theory 19 (2009), No. 1, 001--027
Copyright Heldermann Verlag 2009

Composition Series for a Family of Modules of Nongraded Hamiltonial Type Lie Algebras

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

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.

Keywords: Nongraded Hamiltonial type Lie algebras, representations of nongraded Hamiltonial type Lie algebras.

MSC: 17B10, 17B65

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