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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Properness of Lie algebras and enveloping algebras. I


Author: Walter Michaelis
Journal: Proc. Amer. Math. Soc. 101 (1987), 17-23
MSC: Primary 17B35; Secondary 16A24, 17B10
DOI: https://doi.org/10.1090/S0002-9939-1987-0897064-1
MathSciNet review: 897064
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Abstract: An associative unitary (respectively, Lie) algebra is said to be proper in case the intersection of ail of its cofinite two-sided (respectively, Lie) ideals is zero. Using the Hopf algebra structure of $ UL$, it is shown that over a field of characteristic zero a Lie algebra is proper if and only if its universal enveloping algebra is proper. (In the finite-dimensional case this provides a new proof of a result of Harish-Chandra.) The analogous result for Lie $ p$-algebras and their restricted universal enveloping algebras holds and is proved by the same technique.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0897064-1
Article copyright: © Copyright 1987 American Mathematical Society

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