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
DOI:
https://doi.org/10.1090/S0002-9939-1978-0469992-7
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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- [3] John P. Labute, Algèbres de Lie et pro-p-groupes définis par une seule relation, Invent. Math. 4 (167), 142-158. MR 36 #1581. MR 0218495 (36:1581)
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-, The lower central series of the group
(to appear).
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Additional Information
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