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Proceedings of the American Mathematical Society

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

 
 

 

The semicenter of an enveloping algebra is factorial


Authors: Lieven Le Bruyn and Alfons I. Ooms
Journal: Proc. Amer. Math. Soc. 93 (1985), 397-400
MSC: Primary 17B35
DOI: https://doi.org/10.1090/S0002-9939-1985-0773989-0
MathSciNet review: 773989
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Abstract: Let $ L$ be a finite-dimensional Lie algebra over a field $ k$ of characteristic zero, and $ U(L)$ its universal enveloping algebra. We show that the semicenter of $ U(L)$ is a UFD. More generally, the same result holds when $ k$ is replaced by any factorial ring $ R$ of characteristic zero.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0773989-0
Keywords: Finite-dimensional Lie algebra, universal enveloping algebra, semicenter, factorial ring
Article copyright: © Copyright 1985 American Mathematical Society

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