Date of Award
1992
Publication Type
Master Thesis
Degree Name
M.Sc.
Department
Mathematics and Statistics
Keywords
Mathematics.
Rights
info:eu-repo/semantics/openAccess
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Abstract
For any simple Lie algebra L with any maximal toral subalgebra H, the classification of all simple H diagonalizable L modules having a finite dimensional weight space 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 $A\sb{n-1}$ and $C\sb{m}$. For the case of $A\sb{n-1}$ we show that there are no simple torsion free $A\sb{n-1}$ modules of degree k for $n\ge5$ and $2\le k\le n - 3.$ We conclude with some examples showing that there exist simple torsion free $A\sb{n-1}$ modules of degrees 1, $n - 2$ and $n - 1,$ whenever $n\ge3.$Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1992 .T376. Source: Masters Abstracts International, Volume: 31-04, page: 1811. Thesis (M.Sc.)--University of Windsor (Canada), 1992.
Recommended Citation
Tarokh, Vahid., "A constraint on existence of torsion free lie modules." (1992). Electronic Theses and Dissertations. 575.
https://scholar.uwindsor.ca/etd/575