
Journal of Lie Theory 19 (2009), No. 1, 001027 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 yufeng@math.pku.edu.cn Nongraded infinitedimensional simple Lie algebras of Hamiltonial type were constructed by Xu related to pairs of locallyfinite 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 finitedimensional irreducible modules of symplectic Lie algebras. When the corresponding modules of symplectic Lie algebras are finitedimensional irreducible weight modules whose weight spaces are all onedimensional, 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 [ Fulltextpdf (240 KB)] for subscribers only. 