# A constraint on the existence of simple torsion-free lie modules

Published

Journal Article

For any simple Lie algebra L with Cartan subalgebra H the classification of all simple H-diagonalizable. H-modules having a finite-dimensional weight space is known to depend on determining the simple torsion-free Lmodules 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 An and Cn. For the case of An. we show that there are no simple torsion-free An- modules of degree k for n ≥ 4 and 2 ≤ k ≤ n - 2. We conclude with some examples showing that there exist simple torsion-free A. -modules of degrees 1, n - 1, and n. © 1995 American Mathematical Society.

### Full Text

### Duke Authors

### Cited Authors

- Britten, D; Lemire, F; Tarokh, V

### Published Date

- January 1, 1995

### Published In

### Volume / Issue

- 123 / 8

### Start / End Page

- 2315 - 2321

### Electronic International Standard Serial Number (EISSN)

- 1088-6826

### International Standard Serial Number (ISSN)

- 0002-9939

### Digital Object Identifier (DOI)

- 10.1090/S0002-9939-1995-1246518-1

### Citation Source

- Scopus