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Proceedings of the American Mathematical Society

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

 

 

Free Lie algebras as modules over their enveloping algebras


Author: John P. Labute
Journal: Proc. Amer. Math. Soc. 68 (1978), 135-139
MSC: Primary 17B35
MathSciNet review: 0469992
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Abstract: In this paper we determine the linear relations that exist between the free generators of a free Lie algebra L when it is viewed as a module over its enveloping algebra via the adjoint representation. As an application, the annihilator of a homogeneous element of L is determined.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0469992-7
Keywords: Free Lie algebra, adjoint representation, annihilator
Article copyright: © Copyright 1978 American Mathematical Society