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On a class of finite-dimensional Lie algebras


Author: Ralph K. Amayo
Journal: Proc. Amer. Math. Soc. 78 (1980), 193-197
MSC: Primary 17B65; Secondary 16A64, 17B15
DOI: https://doi.org/10.1090/S0002-9939-1980-0550492-X
MathSciNet review: 550492
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Abstract: Over fields of prime characteristic the centre of the universal enveloping algebra of a finite-dimensional Lie algebra contains a finitely generated polynomial algebra over which the universal envelope is a finitely generated module. This result, which is due to Curtis, is crucial in certain investigations of finitely generated soluble Lie algebras and motivates the introduction of the class Max-cu, which will be called the class of Curtis algebras, consisting of Lie algebras whose universal envelopes have the property described above. It has been an open question whether the class Max-cu consists of finite-dimensional Lie algebras. This paper gives an affirmative answer to the question.


References [Enhancements On Off] (What's this?)

  • [1] R. K. Amayo and I. N. Stewart, Infinite-dimensional Lie algebras, Noordhoff, Leyden, 1974.
  • [2] -, Finitely generated Lie algebras, J. London Math. Soc. 5 (1972), 697-703. MR 0323850 (48:2205)
  • [3] R. K. Amayo, Engel Lie rings with chain conditions, Pacific J. Math. 54 (1974), 1-12. MR 0360727 (50:13174)
  • [4] C. W. Curtis, Noncommutative extensions of Hilbert rings, Proc. Amer. Math. Soc. 4 (1953), 945-955. MR 0059254 (15:498g)
  • [5] N. Jacobson, Lie algebras, Interscience, New York, 1962. MR 0143793 (26:1345)

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DOI: https://doi.org/10.1090/S0002-9939-1980-0550492-X
Article copyright: © Copyright 1980 American Mathematical Society

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