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

Nongraded infinite-dimensional simple Lie algebras of Hamiltonial type were constructed by Xu related to pairs of locally-finite derivations oil certain commutative associative algebras. In this paper, we construct a family of modules with parameters for nongraded Hamiltonial type Lie algebras based oil 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 all explicit construction of the composition series are also given by means of the exterior algebra powers.