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

Publication
, Journal Article

Britten, D; Lemire, F; Tarokh, V

Published in: Proceedings of the American Mathematical Society

January 1, 1995

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.

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## Published In

Proceedings of the American Mathematical Society

## DOI

## EISSN

1088-6826

## ISSN

0002-9939

## Publication Date

January 1, 1995

## Volume

123

## Issue

8

## Start / End Page

2315 / 2321

## Related Subject Headings

- 4904 Pure mathematics
- 0101 Pure Mathematics

### Citation

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Chicago

ICMJE

MLA

NLM

Britten, D., Lemire, F., & Tarokh, V. (1995). A constraint on the existence of simple torsion-free lie modules.

*Proceedings of the American Mathematical Society*,*123*(8), 2315–2321. https://doi.org/10.1090/S0002-9939-1995-1246518-1Britten, D., F. Lemire, and V. Tarokh. “A constraint on the existence of simple torsion-free lie modules.”

*Proceedings of the American Mathematical Society*123, no. 8 (January 1, 1995): 2315–21. https://doi.org/10.1090/S0002-9939-1995-1246518-1.Britten D, Lemire F, Tarokh V. A constraint on the existence of simple torsion-free lie modules. Proceedings of the American Mathematical Society. 1995 Jan 1;123(8):2315–21.

Britten, D., et al. “A constraint on the existence of simple torsion-free lie modules.”

*Proceedings of the American Mathematical Society*, vol. 123, no. 8, Jan. 1995, pp. 2315–21.*Scopus*, doi:10.1090/S0002-9939-1995-1246518-1.Britten D, Lemire F, Tarokh V. A constraint on the existence of simple torsion-free lie modules. Proceedings of the American Mathematical Society. 1995 Jan 1;123(8):2315–2321.

## Published In

Proceedings of the American Mathematical Society

## DOI

## EISSN

1088-6826

## ISSN

0002-9939

## Publication Date

January 1, 1995

## Volume

123

## Issue

8

## Start / End Page

2315 / 2321

## Related Subject Headings

- 4904 Pure mathematics
- 0101 Pure Mathematics