Universal enveloping algebras with subexponential but not polynomially bounded growth
Author:
Martha K. Smith
Journal:
Proc. Amer. Math. Soc. 60 (1976), 22-24
MSC:
Primary 16A68; Secondary 17B35
DOI:
https://doi.org/10.1090/S0002-9939-1976-0419534-5
MathSciNet review:
0419534
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Abstract | References | Similar Articles | Additional Information
Abstract: The universal enveloping algebras of certain Lie algebras provide examples of integral domains with growth which is subexponential but not bounded by any polynomial.
- H. Bass, The degree of polynomial growth of finitely generated nilpotent groups, Proc. London Math. Soc. (3) 25 (1972), 603–614. MR 379672, DOI https://doi.org/10.1112/plms/s3-25.4.603
- 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 Co., 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), 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
Keywords:
Subexponential growth,
polynomially bounded growth,
universal enveloping algebra
Article copyright:
© Copyright 1976
American Mathematical Society
