Abstract
It is proven that a finitely generated soluble-by-finite Lie algebra has a subexponential growth. This implies that in its universal envelope every subring is an Ore domain.
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References
Ralph K. Amayo and Ian Stewart,Infinite Dimensional Lie Algebras, Noordhoff Int. publishing, 1974.
W. Borho and H. Kraft,Uber die Gelfand—Kirillov Dimension, Math. Ann.220 (1976), 1–24.
P. M. Cohn,Free Rings and their Relations, Academic Press, London-New York, 1971.
N. Jacobson,Lie Algebras, Wiley, New York and London, 1962.
A. I. Lichtman,On matrix rings and linear groups over fields of fractions of groups rings and enveloping algebras I, J. Algebra, to appear.
J. Milnor,A note on curvature and fundamental groups, J. Differ. Geom.2 (1968), 1–7.
A. L. Šmelkin,Wreath products of Lie algebras and their application in the theory of groups, Trans. Moscow Math. Soc.29 (1973), 247–260 (in Russian).
Martha K. Smith,Universal enveloping algebras with subexponential but not polynomially bounded growth, Proc. Am. Math. Soc.60 (1976), 22–24.
Martha K. Smith,Growth of algebras, inRing Theory II (Proceedings of the Second Oklahoma Conference) (B. R. McDonald and R. A. Morris, eds.), Marcel Dekker, New York, 1977, pp. 247–259.
J. Wolf,Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differ. Geom.2 (1968), 421–446.
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Lichtman, A.I. Growth in enveloping algebras. Israel J. Math. 47, 296–304 (1984). https://doi.org/10.1007/BF02760603
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DOI: https://doi.org/10.1007/BF02760603