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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Injective hulls of simple $ \mathrm{sl}(2, \mathcal{C})$ modules are locally Artinian


Author: Randall P. Dahlberg
Journal: Proc. Amer. Math. Soc. 107 (1989), 35-37
MSC: Primary 17B35
MathSciNet review: 965241
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Abstract: Let $ L$ denote the simple Lie algebra $ {\text{sl(2,}}{\mathbf{C}}{\text{)}}$ over the complex numbers $ {\mathbf{C}}$. For any simple $ L$-modules $ S$, considered as a left unital module over the universal enveloping algebra of $ L,U(L)$, the injective hull of $ S,{E_L}(S)$, is a locally Artinian $ U(L)$-module.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0965241-9
PII: S 0002-9939(1989)0965241-9
Article copyright: © Copyright 1989 American Mathematical Society