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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On a class of finite-dimensional Lie algebras
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by Ralph K. Amayo PDF
Proc. Amer. Math. Soc. 78 (1980), 193-197 Request permission

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.
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Additional Information
  • © Copyright 1980 American Mathematical Society
  • 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