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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Universal enveloping algebras with subexponential but not polynomially bounded growth
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by Martha K. Smith PDF
Proc. Amer. Math. Soc. 60 (1976), 22-24 Request permission


The universal enveloping algebras of certain Lie algebras provide examples of integral domains with growth which is subexponential but not bounded by any polynomial.
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  • I. M. Gelfand and A. A. Kirillov, Sur les corps liés aux algèbres enveloppantes des algèbres de Lie, Inst. Hautes Études Sci. Publ. Math. 31 (1966), 5–19 (French). MR 207918
  • Emil Grosswald, Topics from the theory of numbers, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0228408
  • Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793
  • J. Milnor, Problem 5603, Amer. Math. Monthly 75 (1968), 685-686.
  • Joseph A. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geometry 2 (1968), 421–446. MR 248688
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 22-24
  • MSC: Primary 16A68; Secondary 17B35
  • DOI:
  • MathSciNet review: 0419534