## Electronic Theses and Dissertations

1995

Master Thesis

M.Sc.

#### Department

Mathematics and Statistics

Mathematics.

#### Rights

info:eu-repo/semantics/openAccess

Let L denote a finite dimensional simple Lie algebra over the complex numbers $\doubc$ having a Cartan subalgebra ${\cal H}$. The classification of all simple ${\cal H}$-diagonalizable L-modules having all finite dimensional weight spaces is known to depend on determining the simple torsion free L-modules of finite degree. It is further known that the only simple Lie algebras which admit simple torsion free modules of finite degree are those of types A and C. For the case of $C\sb2$ we prove that every indecomposable torsion free $C\sb2$-module of degree 2 is simple and it is equivalent to a submodule of the tensor product of a pointed torsion free $C\sb2$-module with a finite dimensional $C\sb2$-module.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1995 .C43. Source: Masters Abstracts International, Volume: 34-02, page: 0769. Thesis (M.Sc.)--University of Windsor (Canada), 1995.