Free Lie algebras as modules over their enveloping algebras
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- by John P. Labute PDF
- Proc. Amer. Math. Soc. 68 (1978), 135-139 Request permission
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.References
- N. Bourbaki, Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1349, Hermann, Paris, 1972. MR 0573068
- Marshall Hall Jr., A basis for free Lie rings and higher commutators in free groups, Proc. Amer. Math. Soc. 1 (1950), 575–581. MR 38336, DOI 10.1090/S0002-9939-1950-0038336-7
- John P. Labute, Algèbres de Lie et pro-$p$-groupes définis par une seule relation, Invent. Math. 4 (1967), 142–158 (French). MR 218495, DOI 10.1007/BF01425247 —, The lower central series of the group $\langle x,y:{x^p} = 1\rangle$ (to appear). W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Interscience, New York, 1966.
Additional Information
- © Copyright 1978 American Mathematical Society
- 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