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A classification of simple Lie modules having a $ 1$-dimensional weight space


Authors: D. J. Britten and F. W. Lemire
Journal: Trans. Amer. Math. Soc. 299 (1987), 683-697
MSC: Primary 17B10; Secondary 17B20
DOI: https://doi.org/10.1090/S0002-9947-1987-0869228-9
MathSciNet review: 869228
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Abstract: Let $ L$ denote a simple Lie algebra over the complex numbers. In this paper, we classify and construct all simple $ L$ modules which may be infinite dimensional but have at least one $ 1$-dimensional weight space. This completes the study begun earlier by the authors for the case of $ L = {A_n}$. The approach presented here relies heavily on the results of Suren Fernando whose dissertation dealt with simple weight modules and their weight systems.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0869228-9
Keywords: Simple Lie modules, weight space decomposition, torsion free module
Article copyright: © Copyright 1987 American Mathematical Society

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