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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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