## Lie algebra modules with finite-dimensional weight spaces. I

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- by S. L. Fernando
- Trans. Amer. Math. Soc.
**322**(1990), 757-781 - DOI: https://doi.org/10.1090/S0002-9947-1990-1013330-8
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## Abstract:

Let $\mathfrak {g}$ denote a reductive Lie algebra over an algebraically closed field of characteristic zero, and let $\mathfrak {h}$ denote a Cartan subalgebra of $\mathfrak {g}$. In this paper we study finitely generated $\mathfrak {g}$-modules that decompose into direct sums of finite dimensional $\mathfrak {h}$-weight spaces. We show that the classification of irreducible modules in this category can be reduced to the classification of a certain class of irreducible modules, those we call torsion free modules. We also show that if $\mathfrak {g}$ is a simple Lie algebra that admits a torsion free module, then $\mathfrak {g}$ is of type $A$ or $C$.## References

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## Bibliographic Information

- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**322**(1990), 757-781 - MSC: Primary 17B10
- DOI: https://doi.org/10.1090/S0002-9947-1990-1013330-8
- MathSciNet review: 1013330